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 by completing the square.\newlined2−2d−27=0d^2 - 2d - 27 = 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 2right chevron icon
Solve a quadratic equation by completing the squareright chevron icon

Full solution

Q. Solve by completing the square.\newlined2−2d−27=0d^2 - 2d - 27 = 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. Rewrite equation and add constant: Rewrite the equation in the form of d2+bd=cd^2 + bd = c. Add 2727 to both sides to move the constant term to the right side of the equation. d2−2d−27+27=0+27d^2 - 2d - 27 + 27 = 0 + 27 d2−2d=27d^2 - 2d = 27
  2. Complete the square: Choose the number to add to both sides to complete the square.\newlineSince (−22)2=1\left(-\frac{2}{2}\right)^2 = 1, add 11 to both sides.\newlined2−2d+1=27+1d^2 − 2d + 1 = 27 + 1\newlined2−2d+1=28d^2 − 2d + 1 = 28
  3. Factor left side: Factor the left side of the equation. \newlined2−2d+1d^2 - 2d + 1 is a perfect square trinomial and can be factored into (d−1)2(d - 1)^2.\newline(d−1)2=28(d - 1)^2 = 28
  4. Take square root: Take the square root of both sides of the equation.\newline(d−1)2=±28\sqrt{(d − 1)^2} = \pm\sqrt{28}\newlined−1=±28d − 1 = \pm\sqrt{28}\newlineSince 28\sqrt{28} simplifies to 4⋅7\sqrt{4\cdot7} which is 2⋅72\cdot\sqrt{7}, we have:\newlined−1=±2⋅7d − 1 = \pm2\cdot\sqrt{7}
  5. Solve for d: Solve for d by adding 11 to both sides of the equation.d−1+1=±27+1d - 1 + 1 = \pm 2\sqrt{7} + 1d=1±27d = 1 \pm 2\sqrt{7}
  6. Calculate decimal values: Calculate the approximate decimal values of dd, rounded to the nearest hundredth.d≈1+27d \approx 1 + 2\sqrt{7} or d≈1−27d \approx 1 - 2\sqrt{7}d≈1+2×2.65d \approx 1 + 2\times2.65 or d≈1−2×2.65d \approx 1 - 2\times2.65d≈1+5.30d \approx 1 + 5.30 or d≈1−5.30d \approx 1 - 5.30d≈6.30d \approx 6.30 or d≈−4.30d \approx -4.30

More problems from Solve a quadratic equation by completing the square

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 1 year ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 1 year ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 9 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 9 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 9 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 9 months ago

View all (179)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant