Algebra Examples

${(x - 4)}^{2} + y^{2} = 16$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

${(x - 4)}^{2} + {(0)}^{2} = 16$

Step 1.2

Solve the equation.

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Step 1.2.1

Subtract ${(0)}^{2}$ from both sides of the equation.

${(x - 4)}^{2} = 16 - {(0)}^{2}$

Step 1.2.2

Raising $0$ to any positive power yields $0$ .

${(x - 4)}^{2} = 16 - 0$

Step 1.2.3

Multiply $- 1$ by $0$ .

${(x - 4)}^{2} = 16 + 0$

Step 1.2.4

Add $16$ and $0$ .

${(x - 4)}^{2} = 16$

Step 1.2.5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x - 4 = \pm \sqrt{16}$

Step 1.2.6

Simplify $\pm \sqrt{16}$ .

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Step 1.2.6.1

Rewrite $16$ as $4^{2}$ .

$x - 4 = \pm \sqrt{4^{2}}$

Step 1.2.6.2

Pull terms out from under the radical, assuming positive real numbers.

$x - 4 = \pm 4$

Step 1.2.7

The complete solution is the result of both the positive and negative portions of the solution.

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Step 1.2.7.1

First, use the positive value of the $\pm$ to find the first solution.

$x - 4 = 4$

Step 1.2.7.2

Move all terms not containing $x$ to the right side of the equation.

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Step 1.2.7.2.1

Add $4$ to both sides of the equation.

$x = 4 + 4$

Step 1.2.7.2.2

Add $4$ and $4$ .

$x = 8$

Step 1.2.7.3

Next, use the negative value of the $\pm$ to find the second solution.

$x - 4 = - 4$

Step 1.2.7.4

Move all terms not containing $x$ to the right side of the equation.

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Step 1.2.7.4.1

Add $4$ to both sides of the equation.

$x = - 4 + 4$

Step 1.2.7.4.2

Add $- 4$ and $4$ .

$x = 0$

Step 1.2.7.5

The complete solution is the result of both the positive and negative portions of the solution.

$x = 8, 0$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(8, 0), (0, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

${((0) - 4)}^{2} + y^{2} = 16$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify ${((0) - 4)}^{2} + y^{2}$ .

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Step 2.2.1.1

Subtract $4$ from $0$ .

${(- 4)}^{2} + y^{2} = 16$

Step 2.2.1.2

Raise $- 4$ to the power of $2$ .

$16 + y^{2} = 16$

Step 2.2.2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.2.1

Subtract $16$ from both sides of the equation.

$y^{2} = 16 - 16$

Step 2.2.2.2

Subtract $16$ from $16$ .

$y^{2} = 0$

Step 2.2.3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{0}$

Step 2.2.4

Simplify $\pm \sqrt{0}$ .

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Step 2.2.4.1

Rewrite $0$ as $0^{2}$ .

$y = \pm \sqrt{0^{2}}$

Step 2.2.4.2

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 0$

Step 2.2.4.3

Plus or minus $0$ is $0$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

Step 3

List the intersections.

x-intercept(s): $(8, 0), (0, 0)$

y-intercept(s): $(0, 0)$

Step 4