Solve by Completing the Square 5x^2-30x=5

$5 x^{2} - 30 x = 5$

Step 1

Divide each term in $5 x^{2} - 30 x = 5$ by $5$ and simplify.

Divide each term in $5 x^{2} - 30 x = 5$ by $5$ .

$\frac{5 x^{2}}{5} + \frac{- 30 x}{5} = \frac{5}{5}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x^{2}}{5} + \frac{- 30 x}{5} = \frac{5}{5}$

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

$x^{2} + \frac{- 30 x}{5} = \frac{5}{5}$

Cancel the common factor of $- 30$ and $5$ .

Factor $5$ out of $- 30 x$ .

$x^{2} + \frac{5 (- 6 x)}{5} = \frac{5}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$x^{2} + \frac{5 (- 6 x)}{5 (1)} = \frac{5}{5}$

Cancel the common factor.

$x^{2} + \frac{5 (- 6 x)}{5 \cdot 1} = \frac{5}{5}$

Rewrite the expression.

$x^{2} + \frac{- 6 x}{1} = \frac{5}{5}$

Divide $- 6 x$ by $1$ .

$x^{2} - 6 x = \frac{5}{5}$

Simplify the right side.

Divide $5$ by $5$ .

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

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.

Simplify the left side.

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

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

Simplify the right side.

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

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

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

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 $x$ .

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

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

Add $3$ to 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:

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

Solve by Completing the Square 5x^2-30x=5

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