How to solve (x-3)^(2)=8(y+5)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (x-3)^(2)=8(y+5) | Equatix

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Question

$${ \left(x-3 \right) }^{ 2 } =8(y+5)$$

Solve for y

$y=\frac{\left(x-3\right)^{2}-40}{8}$

Steps for Solving Linear Equation

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-3\right)^{2}$.

$$x^{2}-6x+9=8\left(y+5\right)$$

Use the distributive property to multiply $8$ by $y+5$.

$$x^{2}-6x+9=8y+40$$

Swap sides so that all variable terms are on the left hand side.

$$8y+40=x^{2}-6x+9$$

Subtract $40$ from both sides.

$$8y=x^{2}-6x+9-40$$

Subtract $40$ from $9$ to get $-31$.

$$8y=x^{2}-6x-31$$

Divide both sides by $8$.

$$\frac{8y}{8}=\frac{x^{2}-6x-31}{8}$$

Dividing by $8$ undoes the multiplication by $8$.

$$y=\frac{x^{2}-6x-31}{8}$$

Divide $x^{2}-6x-31$ by $8$.

$$y=\frac{x^{2}}{8}-\frac{3x}{4}-\frac{31}{8}$$

Show Solution

Solve for x (complex solution)

$x=-2\sqrt{2\left(y+5\right)}+3$
$x=2\sqrt{2\left(y+5\right)}+3$

Solve for x

$x=-2\sqrt{2\left(y+5\right)}+3$
$x=2\sqrt{2\left(y+5\right)}+3\text{, }y\geq -5$