Question

Solve each equation. $$ (2 t-3)^{2}-20=44 $$

   Solve each equation. 
$$
(2 t-3)^{2}-20=44
$$

Impact Mathematics Algebra and More

Impact Mathematics Algebra and More

McGraw Hill 1st Edition

Chapter 7, Problem 15

Instant Answer

Solved by Expert Sriram Soundarrajan

07/03/2020

Step 1

We can do this by adding 20 to both sides of the equation: \[ (2t-3)^2 - 20 + 20 = 44 + 20 \] which simplifies to: \[ (2t-3)^2 = 64 \] Show more…

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Solve each equation. $$ (2 t-3)^{2}-20=44 $$

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Key Concepts

Solving Linear Equations

After applying the square root property, the resulting equations are linear. This concept involves using inverse operations to isolate the variable, turning the equation into a format where the solution can be readily obtained.

Square Root Property

When you have an equation where a squared expression equals a constant, you can solve it by taking the square root of both sides of the equation. It is crucial to consider both the positive and negative square roots because squaring either a positive or negative number gives the same result.

Isolating the Squared Term

This concept involves rearranging an equation to have the squared expression by itself on one side. It simplifies the process of solving equations by setting up a format where the square root property can be directly applied.

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