Solve the equation using square roots. Select the solution(s).
[tex]x^2-55=26[/tex]
Answer (1)
Add 55 to both sides of the equation: x 2 = 26 + 55 .
Simplify: x 2 = 81 .
Take the square root of both sides: x = ± 81 .
Simplify to find the solutions: x = ± 9 . The solutions are 9 , − 9 .
Explanation
Understanding the Problem We are given the equation x 2 − 55 = 26 and asked to solve for x using square roots. Our goal is to isolate x 2 and then take the square root of both sides to find the possible values of x .
Isolating the x^2 term First, we add 55 to both sides of the equation to isolate the x 2 term: x 2 − 55 + 55 = 26 + 55
Simplifying the Equation Simplifying the right side of the equation, we get: x 2 = 81
Taking the Square Root Now, we take the square root of both sides of the equation to solve for x :
x = ± 81
Finding the Solutions Simplifying the square root, we find the two possible solutions for x :
x = ± 9
Final Answer Therefore, the solutions to the equation x 2 − 55 = 26 are x = 9 and x = − 9 .
Examples
Imagine you are designing a square garden and need it to cover a specific area. If the area of the garden is represented by x 2 and you know that x 2 − 55 = 26 , solving this equation will tell you the possible side lengths ( x ) of the garden. This ensures you build the garden to the exact size you planned, demonstrating a practical application of solving quadratic equations using square roots.
