Solve for x x = square root of x^2+7x-3

$x = \sqrt{x^{2} + 7 x - 3}$

Step 1

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\sqrt{x^{2} + 7 x - 3} = x$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x^{2} + 7 x - 3}}^{2} = x^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{2} + 7 x - 3}$ as ${(x^{2} + 7 x - 3)}^{\frac{1}{2}}$ .

${({(x^{2} + 7 x - 3)}^{\frac{1}{2}})}^{2} = x^{2}$

Simplify the left side.

Simplify ${({(x^{2} + 7 x - 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x^{2} + 7 x - 3)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x^{2} + 7 x - 3)}^{\frac{1}{2} \cdot 2} = x^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x^{2} + 7 x - 3)}^{\frac{1}{2} \cdot 2} = x^{2}$

Rewrite the expression.

${(x^{2} + 7 x - 3)}^{1} = x^{2}$

Simplify.

$x^{2} + 7 x - 3 = x^{2}$

Step 4

Solve for $x$ .

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

Subtract $x^{2}$ from both sides of the equation.

$x^{2} + 7 x - 3 - x^{2} = 0$

Combine the opposite terms in $x^{2} + 7 x - 3 - x^{2}$ .

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

$7 x - 3 + 0 = 0$

Add $7 x - 3$ and $0$ .

$7 x - 3 = 0$

Add $3$ to both sides of the equation.

$7 x = 3$

Divide each term in $7 x = 3$ by $7$ and simplify.

Divide each term in $7 x = 3$ by $7$ .

$\frac{7 x}{7} = \frac{3}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{3}{7}$

Divide $x$ by $1$ .

$x = \frac{3}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{7}$

Decimal Form:

$x = 0.\overline{428571}$

Solve for x x = square root of x^2+7x-3

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