Solve Using the Quadratic Formula x(x+3)=5x+3

$x (x + 3) = 5 x + 3$

Step 1

Move all terms to the left side of the equation and simplify.

Simplify the left side.

Simplify $x (x + 3)$ .

Apply the distributive property.

$x \cdot x + x \cdot 3 = 5 x + 3$

Simplify the expression.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 = 5 x + 3$

Move $3$ to the left of $x$ .

$x^{2} + 3 x = 5 x + 3$

Move all the expressions to the left side of the equation.

Subtract $5 x$ from both sides of the equation.

$x^{2} + 3 x - 5 x = 3$

Subtract $3$ from both sides of the equation.

$x^{2} + 3 x - 5 x - 3 = 0$

Subtract $5 x$ from $3 x$ .

$x^{2} - 2 x - 3 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 2$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (1 \cdot - 3)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 3}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 3$ .

Multiply $- 4$ by $1$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot - 3}}{2 \cdot 1}$

Multiply $- 4$ by $- 3$ .

$x = \frac{2 \pm \sqrt{4 + 12}}{2 \cdot 1}$

Add $4$ and $12$ .

$x = \frac{2 \pm \sqrt{16}}{2 \cdot 1}$

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

$x = \frac{2 \pm \sqrt{4^{2}}}{2 \cdot 1}$

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

$x = \frac{2 \pm 4}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{2 \pm 4}{2}$

Simplify $\frac{2 \pm 4}{2}$ .

$x = 1 \pm 2$

Step 5

The final answer is the combination of both solutions.

$x = 3, - 1$

Solve Using the Quadratic Formula x(x+3)=5x+3

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