Finite Math Examples

$x (x + 3) - 2 = 3 x + 23$

Step 1

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

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$x \cdot x + x \cdot 3 - 2 = 3 x + 23$

Step 1.1.1.2

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 - 2 = 3 x + 23$

Step 1.1.1.3

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

$x^{2} + 3 x - 2 = 3 x + 23$

Step 1.2

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

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Step 1.2.1

Subtract $3 x$ from both sides of the equation.

$x^{2} + 3 x - 2 - 3 x = 23$

Step 1.2.2

Subtract $23$ from both sides of the equation.

$x^{2} + 3 x - 2 - 3 x - 23 = 0$

Step 1.3

Simplify $x^{2} + 3 x - 2 - 3 x - 23$ .

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Step 1.3.1

Combine the opposite terms in $x^{2} + 3 x - 2 - 3 x - 23$ .

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Step 1.3.1.1

Subtract $3 x$ from $3 x$ .

$x^{2} + 0 - 2 - 23 = 0$

Step 1.3.1.2

Add $x^{2}$ and $0$ .

$x^{2} - 2 - 23 = 0$

Step 1.3.2

Subtract $23$ from $- 2$ .

$x^{2} - 25 = 0$

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 $a = 1$ , $b = 0$ , and $c = - 25$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 25)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 25}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 25$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 25}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 25$ .

$x = \frac{0 \pm \sqrt{0 + 100}}{2 \cdot 1}$

Step 4.1.3

Add $0$ and $100$ .

$x = \frac{0 \pm \sqrt{100}}{2 \cdot 1}$

Step 4.1.4

Rewrite $100$ as $10^{2}$ .

$x = \frac{0 \pm \sqrt{10^{2}}}{2 \cdot 1}$

Step 4.1.5

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

$x = \frac{0 \pm 10}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{0 \pm 10}{2}$

Step 4.3

Simplify $\frac{0 \pm 10}{2}$ .

$x = \pm 5$

Step 5

The final answer is the combination of both solutions.

$x = 5, - 5$