Question

Solve the equation. $$ (t+2)^{2}=(t-4)^{2} $$

   Solve the equation.
$$
(t+2)^{2}=(t-4)^{2}
$$

College Algebra Essentials

College Algebra Essentials

Julie Miller 1st Edition

Chapter 1, Problem 101

Instant Answer

Solved by Expert Erika Bustos

08/07/2021

Step 1

This gives us: $$ t^2 + 4t + 4 = t^2 - 8t + 16 $$ Show more…

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Solve the equation. $$ (t+2)^{2}=(t-4)^{2} $$

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Key Concepts

Solving Linear Equations

Once the square equality is separated into its two potential linear equations, each resulting equation involves only linear terms. Solving these linear equations typically involves isolating the variable through basic algebraic manipulations, a foundational technique in algebra for finding the solutions to the problem.

Property of Equality of Squares

When two expressions squared are equal, it implies that either the expressions themselves are equal or they are negatives of each other. This property is used to simplify equations of the form a² = b² into the two cases a = b or a = -b, ensuring that all possible solutions are considered.

Absolute Value Interpretation

Squaring an expression removes its sign, which can be interpreted using absolute values. Recognizing that an equation of the form a² = b² translates to |a| = |b| helps in understanding why both a positive and a negative match must be evaluated, reinforcing the need to consider both cases when solving such equations.

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