Algebra Examples

$4 x^{2} + 24 x = 4$

Step 1

Divide each term in $4 x^{2} + 24 x = 4$ by $4$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $4 x^{2} + 24 x = 4$ by $4$ .

$\frac{4 x^{2}}{4} + \frac{24 x}{4} = \frac{4}{4}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.2.1.1.1

Cancel the common factor.

$\frac{4 x^{2}}{4} + \frac{24 x}{4} = \frac{4}{4}$

Step 1.2.1.1.2

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{24 x}{4} = \frac{4}{4}$

Step 1.2.1.2

Cancel the common factor of $24$ and $4$ .

Tap for more steps...

Step 1.2.1.2.1

Factor $4$ out of $24 x$ .

$x^{2} + \frac{4 (6 x)}{4} = \frac{4}{4}$

Step 1.2.1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1.2.2.1

Factor $4$ out of $4$ .

$x^{2} + \frac{4 (6 x)}{4 (1)} = \frac{4}{4}$

Step 1.2.1.2.2.2

Cancel the common factor.

$x^{2} + \frac{4 (6 x)}{4 \cdot 1} = \frac{4}{4}$

Step 1.2.1.2.2.3

Rewrite the expression.

$x^{2} + \frac{6 x}{1} = \frac{4}{4}$

Step 1.2.1.2.2.4

Divide $6 x$ by $1$ .

$x^{2} + 6 x = \frac{4}{4}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Divide $4$ by $4$ .

$x^{2} + 6 x = 1$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(3)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 6 x + {(3)}^{2} = 1 + {(3)}^{2}$

Step 4

Simplify the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = 1 + {(3)}^{2}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $1 + {(3)}^{2}$ .

Tap for more steps...

Step 4.2.1.1

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = 1 + 9$

Step 4.2.1.2

Add $1$ and $9$ .

$x^{2} + 6 x + 9 = 10$

Step 5

Factor the perfect trinomial square into ${(x + 3)}^{2}$ .

${(x + 3)}^{2} = 10$

Step 6

Solve the equation for $x$ .

Tap for more steps...

Step 6.1

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

$x + 3 = \pm \sqrt{10}$

Step 6.2

Subtract $3$ from both sides of the equation.

$x = \pm \sqrt{10} - 3$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{10} - 3$

Decimal Form:

$x = 0.16227766 \dots, - 6.16227766 \dots$