Solve for x 1/5x^2+2=3/5x^2

$\frac{1}{5} x^{2} + 2 = \frac{3}{5} x^{2}$

Step 1

Combine $\frac{1}{5}$ and $x^{2}$ .

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

Step 2

Combine $\frac{3}{5}$ and $x^{2}$ .

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

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $\frac{3 x^{2}}{5}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $3 x^{2}$ from $x^{2}$ .

$2 + \frac{- 2 x^{2}}{5} = 0$

Move the negative in front of the fraction.

$2 - \frac{2 x^{2}}{5} = 0$

Step 4

Subtract $2$ from both sides of the equation.

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

Step 5

Multiply both sides of the equation by $- \frac{5}{2}$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{2} (- \frac{2 x^{2}}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Move the leading negative in $- \frac{2 x^{2}}{5}$ into the numerator.

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

Factor $5$ out of $- 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

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

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

Simplify the right side.

Simplify $- \frac{5}{2} \cdot - 2$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x^{2} = - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

$x^{2} = 5$

Step 7

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

$x = \pm \sqrt{5}$

Step 8

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{5}, - \sqrt{5}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5}, - \sqrt{5}$

Decimal Form:

$x = 2.23606797 \dots, - 2.23606797 \dots$

Solve for x 1/5x^2+2=3/5x^2

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