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.\newlineh2+20h=−49h^2 + 20h = -49\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____

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.\newlineh2+20h=−49h^2 + 20h = -49\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____
  1. Rewrite Equation: h2+20h=−49h^2 + 20h = -49\newlineRewrite the equation in the form of h2+bh=ch^2 + bh = c.\newlineAdd 4949 to both sides to set the equation to zero.\newlineh2+20h+49=0h^2 + 20h + 49 = 0
  2. Complete the Square: h2+20h+49=0h^2 + 20h + 49 = 0\newlineChoose the number to add to both sides to complete the square.\newlineSince (20/2)2=100(20/2)^2 = 100, add 100100 to both sides.\newlineh2+20h+100=49+100h^2 + 20h + 100 = 49 + 100\newlineh2+20h+100=149h^2 + 20h + 100 = 149
  3. Identify Factored Equation: h2+20h+100=149h^2 + 20h + 100 = 149\newlineIdentify the equation after factoring the left side.\newlineh2+20h+100=149h^2 + 20h + 100 = 149\newline(h+10)2=149(h + 10)^2 = 149
  4. Take Square Root: h+10)2=149(h + 10)^2 = 149(\newlineIdentify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline\$\sqrt{(h + 10)^2} = \sqrt{149}\)\(\newline\)h + \(10\) = \pm\sqrt{\(149\)}
  5. Isolate Variable: We found:\(\newline\)\(h + 10 = \pm\sqrt{149}\)\(\newline\)Choose the equation after isolating the variable h.\(\newline\)To isolate h, subtract \(10\) from both sides of the equation.\(\newline\)\(h + 10 - 10 = \pm\sqrt{149} - 10\)\(\newline\)h = \(-10\) \pm \sqrt{\(149\)}
  6. Find Values of h: We have:\(\newline\)\(h = -10 \pm \sqrt{149}\)\(\newline\)What are the two values of h?\(\newline\)\(h = -10 + \sqrt{149}\) implies \(h \approx -10 + 12.21\) which is \(h \approx 2.21\).\(\newline\)\(h = -10 - \sqrt{149}\) implies \(h \approx -10 - 12.21\) which is \(h \approx -22.21\).\(\newline\)Values of h: \(2.21\), \(-22.21\)

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