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.\newline2d2+4d+1=02d^2 + 4d + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlined=d = _____ or d=d = _____

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.\newline2d2+4d+1=02d^2 + 4d + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlined=d = _____ or d=d = _____
  1. Identify values: Identify the values of aa, bb, and cc in the quadratic equation 2d2+4d+1=02d^2 + 4d + 1 = 0. By comparing the equation to the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=2a = 2 b=4b = 4 c=1c = 1
  2. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula to find dd. The quadratic formula is d=−b±b2−4ac2ad = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So we have: d=−(4)±(4)2−4⋅2⋅12⋅2d = \frac{-(4) \pm \sqrt{(4)^2 - 4\cdot2\cdot1}}{2\cdot2}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (4)2−4⋅2⋅1=16−8=8\sqrt{(4)^2 - 4\cdot 2\cdot 1} = \sqrt{16 - 8} = \sqrt{8}
  4. Simplify formula: Simplify the quadratic formula with the values we have.\newlined=−4±84d = \frac{-4 \pm \sqrt{8}}{4}\newlineSince 8\sqrt{8} can be simplified to 222\sqrt{2}, we can rewrite the equation as:\newlined=−4±224d = \frac{-4 \pm 2\sqrt{2}}{4}
  5. Divide by 44: Simplify the equation further by dividing both terms in the numerator by 44.d=(−1±(12)2)d = (-1 \pm (\frac{1}{2})\sqrt{2})
  6. Round values: If necessary, round the values of dd to the nearest hundredth. The decimal approximation of 2\sqrt{2} is about 1.411.41. So we have: d=−1+(1/2)×1.41d = -1 + (1/2)\times1.41 or d=−1−(1/2)×1.41d = -1 - (1/2)\times1.41 d≈−1+0.705d \approx -1 + 0.705 or d≈−1−0.705d \approx -1 - 0.705 d≈−0.295d \approx -0.295 or d≈−1.705d \approx -1.705

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)