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.\newliney2−4y=25y^2 - 4y = 25\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____

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.\newliney2−4y=25y^2 - 4y = 25\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____
  1. Rewrite in standard form: Write the equation in the form of y2+by=cy^2 + by = c. The given equation is y2−4y=25y^2 - 4y = 25.
  2. Move constant term: Move the constant term to the other side of the equation.\newlineSubtract 2525 from both sides to isolate the yy terms.\newliney2−4y−25=0y^2 - 4y - 25 = 0\newliney2−4y=−25y^2 - 4y = -25
  3. Complete the square: Complete the square by adding the square of half the coefficient of yy to both sides.\newlineThe coefficient of yy is −4-4, so half of that is −2-2, and the square of −2-2 is 44.\newlineAdd 44 to both sides of the equation.\newliney2−4y+4=−25+4y^2 - 4y + 4 = -25 + 4\newliney2−4y+4=−21y^2 - 4y + 4 = -21
  4. Factor left side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial.\newline(y−2)2=−21(y - 2)^2 = -21
  5. Take square root: Take the square root of both sides of the equation.\newlineRemember to include the ±\pm symbol when taking the square root of both sides.\newline(y−2)2=±−21\sqrt{(y - 2)^2} = \pm\sqrt{-21}\newliney−2=±−21y - 2 = \pm\sqrt{-21}
  6. No real solutions: Since the square root of a negative number is not a real number, there are no real solutions to this equation.\newlineThe equation y2−4y=25y^2 - 4y = 25 does not have real solutions because you cannot take the square root of a negative number in the real number system.

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 month 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 month 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 1 month 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 1 month 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 1 month 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 1 month 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 2 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 2 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 2 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 2 months ago

View all (180)