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.\newline4u2+6u+1=04u^2 + 6u + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____

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.\newline4u2+6u+1=04u^2 + 6u + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____
  1. Identify values: Identify the values of aa, bb, and cc in the quadratic equation 4u2+6u+1=04u^2 + 6u + 1 = 0. The quadratic equation is in the form au2+bu+c=0au^2 + bu + c = 0, so by comparison: a=4a = 4 b=6b = 6 c=1c = 1
  2. Substitute in formula: Substitute the values of aa, bb, and cc into the quadratic formula to find uu. The quadratic formula is u=−b±b2−4ac2au = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get: u=−(6)±(6)2−4⋅4⋅12⋅4u = \frac{-(6) \pm \sqrt{(6)^2 - 4\cdot4\cdot1}}{2\cdot4}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (6)2−4⋅4⋅1=36−16=20\sqrt{(6)^2 - 4\cdot 4\cdot 1} = \sqrt{36 - 16} = \sqrt{20}
  4. Continue simplifying: Continue simplifying the quadratic formula with the values we have.\newlineu=−6±208u = \frac{-6 \pm \sqrt{20}}{8}\newlineSince 20\sqrt{20} can be simplified to 252\sqrt{5}, we can rewrite the equation as:\newlineu=−6±258u = \frac{-6 \pm 2\sqrt{5}}{8}
  5. Divide by 22: Simplify the expression by dividing both terms in the numerator by 22.\newlineu=−3±54u = \frac{-3 \pm \sqrt{5}}{4}
  6. Identify possible values: Identify the two possible values for uu.u=−3+54u = \frac{{-3 + \sqrt{5}}}{{4}} or u=−3−54u = \frac{{-3 - \sqrt{5}}}{{4}}
  7. Round to nearest hundredth: Round the values of uu to the nearest hundredth, if necessary.u≈(−3+2.244)u \approx (\frac{-3 + 2.24}{4}) or u≈(−3−2.244)u \approx (\frac{-3 - 2.24}{4})u≈−0.764u \approx \frac{-0.76}{4} or u≈−5.244u \approx \frac{-5.24}{4}u≈−0.19u \approx -0.19 or u≈−1.31u \approx -1.31

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)