Question $(x+5)^{2}-16=0$

Studdy Solution

STEP 1

1. The equation $(x+5)^2 - 16 = 0$ is a quadratic equation in disguise.
2. Solving the equation will involve isolating the squared term and then taking the square root.

STEP 2

1. Isolate the squared term.
2. Take the square root of both sides.
3. Solve for $x$ .

STEP 3

Start by isolating the squared term $(x+5)^2$ on one side of the equation. Add 16 to both sides:
$(x+5)^2 - 16 + 16 = 0 + 16$ $(x+5)^2 = 16$

STEP 4

Take the square root of both sides to solve for $x+5$ . Remember that taking the square root introduces both a positive and a negative solution:
$\sqrt{(x+5)^2} = \pm \sqrt{16}$ $x+5 = \pm 4$

STEP 5

Solve for $x$ by considering both the positive and negative solutions:
For the positive solution: $x+5 = 4$ Subtract 5 from both sides: $x = 4 - 5$ $x = -1$
For the negative solution: $x+5 = -4$ Subtract 5 from both sides: $x = -4 - 5$ $x = -9$
The solutions for $x$ are:
$x = -1 \quad \text{and} \quad x = -9$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms