The equation is What is the larger solution to this equation?

Solution available with step-by-step explanation

SAT Nonlinear Equations & Systems Question 16 | Free SAT Prep | Aniko

00:00

Question 16·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

0 / 233

The equation is

(x + 4)^2 = 100

What is the larger solution to this equation?

Your answer

(Express the answer as an integer)

For equations of the form $(x + a)^2 = b$ , recognize this as a simple quadratic in vertex form. Take the square root of both sides, remembering to include both the positive and negative roots, which gives $x + a = \text{plus/minus} \text{ the square root}$ . Then solve the two resulting linear equations. When a question asks for the larger or smaller solution, make sure you list both solutions clearly and compare them before answering. This approach is faster and less error-prone than expanding the square and using factoring or the quadratic formula.

Hints

Click me!

Undo the square

You see $(x + 4)^2 = 100$ . What operation undoes a square so you can solve for $x$ ?

Remember both square roots

When you take the square root of $100$ , do you get only one value, or should you consider both a positive and a negative value?

Solve and compare

After you turn the problem into two simple linear equations (one with $+10$ and one with $-10$ ), solve both and then decide which solution is greater.

Desmos Guide

Graph both sides of the equation

In Desmos, enter y = (x + 4)^2 on one line and y = 100 on another line. You will see a parabola and a horizontal line.

Find the intersection points

Click on each point where the parabola and the horizontal line intersect. Desmos will show the coordinates of these intersection points; note both $x$ -values.

Identify the larger solution

Compare the two $x$ -values from the intersection points and choose the greater one; that $x$ -value is the larger solution to the equation.

Step-by-step Explanation

Remove the square by taking square roots

Start from the equation

(x + 4)^2 = 100

To undo the square, take the square root of both sides. Remember that the square root of a positive number has two values, positive and negative:

|x + 4| = 10

This means $x + 4$ can be either $10$ or $-10$ .

Set up and partially solve the two linear equations

From $|x+4| = 10$ , write the two equations:

$x + 4 = 10$
$x + 4 = -10$

Now isolate $x$ in each:

For $x + 4 = 10$ : subtract 4 from both sides to get $x = 10 - 4$ .
For $x + 4 = -10$ : subtract 4 from both sides to get $x = -10 - 4$ .

These give two candidate values for $x$ ; evaluate and compare them in the next step.

Evaluate and choose the larger solution

The problem asks for the larger solution.

Compute the values: $10 - 4 = 6$ and $-10 - 4 = -14$ . Compare them: $6$ is greater than $-14$ .

So, the larger solution is 6.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation