Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve using the quadratic formula.\newlinej2−6j+4=0j^2 - 6j + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinej=j = _____ or j=j = _____

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Solve a quadratic equation using the quadratic formularight chevron icon

Full solution

Q. Solve using the quadratic formula.\newlinej2−6j+4=0j^2 - 6j + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinej=j = _____ or j=j = _____
  1. Identify values: Identify the values of aa, bb, and cc in the quadratic equation j2−6j+4=0j^2 − 6j + 4 = 0. The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0. Comparing this with our equation, we get: a=1a = 1 b=−6b = -6 c=4c = 4
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula to find jj. The quadratic formula is j=−b±b2−4ac2aj = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So we have: j=−(−6)±(−6)2−4⋅1⋅42⋅1j = \frac{-(-6) \pm \sqrt{(-6)^2 - 4\cdot1\cdot4}}{2\cdot1}
  3. Simplify expression and constants: Simplify the expression under the square root and the constants outside the square root. \newlinej=6±36−162j = \frac{6 \pm \sqrt{36 - 16}}{2}\newlinej=6±202j = \frac{6 \pm \sqrt{20}}{2}
  4. Factor and simplify square root: Simplify the square root of 2020 by factoring it into 4×54\times5 and taking the square root of 44 out of the square root.20=4×5=2×5\sqrt{20} = \sqrt{4\times5} = 2\times\sqrt{5}Now substitute this back into the equation:j=6±2×52j = \frac{6 \pm 2\times\sqrt{5}}{2}
  5. Divide terms by 22: Simplify the equation by dividing both terms in the numerator by 22.\newlinej=3±52j = \frac{3 \pm \sqrt{5}}{2}
  6. Approximate solutions: Since 5\sqrt{5} cannot be simplified to an integer or a simple fraction, we will leave it as is or round it to the nearest hundredth if necessary.\newlineThe approximate value of 5\sqrt{5} is 2.242.24.\newlineSo the approximate solutions for jj are:\newlinej≈3+2.24j \approx 3 + 2.24 or j≈3−2.24j \approx 3 - 2.24\newlinej≈5.24j \approx 5.24 or j≈0.76j \approx 0.76

More problems from Solve a quadratic equation using the quadratic formula

Question
Solve for v v .\newlinev2+8v+12=0 v^2+8v+12=0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinev= v=_____
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve for u u .\newlineu2=9 u^2 = 9 \newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlineu= u = _____ or u= u = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinek2−20k+_____k^2 - 20k + \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve by completing the square.\newlineu2−24u−23=0u^2 - 24u - 23 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`u` = ________ or `u` =______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the discriminant. \newline2q2−9q+8=02q^2 - 9q + 8 = 0\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=22x−38 y = 22x - 38 \newliney=x2+11x−14 y = x^2 + 11x - 14 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) \newline(_,_) (\_,\_)
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve for aa.\newline(a+5)(a+1)=0(a + 5)(a + 1) = 0\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinea=a = _____ or a=a = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Let p=x2−7 p=x^{2}-7 . Which equation is equivalent to (x2−7)2−4x2+28=5 (x^{2}-7)^{2}-4x^{2}+28=5 in terms of p p ? Choose 11 answer: \newline(A) p2−4p+23=0 p^{2}-4p+23=0 \newline(B) p2+4p−5=0 p^{2}+4p-5=0 \newline(C) p2−4p−5=0 p^{2}-4p-5=0 \newline(D) p2+4p+23=0 p^{2}+4p+23=0
Get tutor helpright-arrow

Posted 2 months ago

Question
Let m=2x+3m=2x+3. Which equation is equivalent to (2x+3)2−14x−21=−6(2x+3)^{2}-14x-21=-6 in terms of mm? Choose 11 answer: \newline(A) m2+7m+6=0m^{2}+7m+6=0 \newline(B) m2−7m−15=0m^{2}-7m-15=0 \newline(C) m2−7m+6=0m^{2}-7m+6=0 \newline(D) m2+7m−15=0m^{2}+7m-15=0
Get tutor helpright-arrow

Posted 2 months ago

Question
Let m=x2+3m=x^{2}+3. Which equation is equivalent to (x2+3)2+7x2+21=−10(x^{2}+3)^{2}+7x^{2}+21=-10 in terms of mm? Choose 11 answer:\newline(A) m2−7m+31=0m^{2}-7m+31=0\newline(B) m2+7m+31=0m^{2}+7m+31=0\newline(C) m2−7m+10=0m^{2}-7m+10=0\newline(D) m2+7m+10=0m^{2}+7m+10=0
Get tutor helpright-arrow

Posted 2 months ago

View all (55)