Solve the equation using square roots. Select the solution(s).
4x^2 - 871 = 29
x = -18 x = -16 x = -14 x = -12
x = -8 x = -6 x^2 = -4 x = -2 x = 0
x = 4 x = 6 x = 5 x = 10
x = 2 no real solution
x = 12 x = 14 x = 16 x = 18
Answer (2)
Add 871 to both sides: 4 x 2 = 900 .
Divide both sides by 4: x 2 = 225 .
Take the square root of both sides: x = ± 225 .
The solutions are x = 15 and x = − 15 , so the answer is x = − 15 , 15 .
Explanation
Isolating the x^2 term First, we need to isolate the x 2 term in the equation 4 x 2 − 871 = 29 . To do this, we add 871 to both sides of the equation: 4 x 2 − 871 + 871 = 29 + 871
Simplifying the equation This simplifies to: 4 x 2 = 900
Dividing by 4 Next, we divide both sides of the equation by 4 to get x 2 by itself: 4 4 x 2 = 4 900
Simplifying further This simplifies to: x 2 = 225
Taking the square root Now, we take the square root of both sides of the equation to solve for x . Remember to consider both the positive and negative square roots: x = ± 225
Finding the solutions Since 225 = 15 , we have two possible solutions for x :
x = 15 or x = − 15
Checking the solutions Finally, we check the solutions against the values in the table. We see that x = 15 and x = − 15 are the solutions.
Examples
Imagine you are designing a square garden and need to determine the length of each side given the total area. This problem demonstrates how to solve for a variable when it is squared, which is essential in many real-world applications, such as calculating areas, volumes, and distances. Understanding how to manipulate equations and use square roots allows you to find the dimensions needed for your garden or any other square-shaped project. This skill is also fundamental in physics and engineering for solving problems related to motion and forces.
To solve the equation 4 x 2 − 871 = 29 , we isolate x 2 , leading to x 2 = 225 . Taking the square root gives x = 15 and x = − 15 , but only x = 15 is among the provided options. Therefore, the final answer is x = 15 .
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