Solve for x square root of x^2+49=x+5

$\sqrt{x^{2} + 49} = x + 5$

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

${\sqrt{x^{2} + 49}}^{2} = {(x + 5)}^{2}$

Simplify each side of the equation.

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Multiply the exponents in ${({(x^{2} + 49)}^{\frac{1}{2}})}^{2}$ .

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

${(x^{2} + 49)}^{\frac{1}{2} \cdot 2} = {(x + 5)}^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

${(x^{2} + 49)}^{\frac{1}{2} \cdot 2} = {(x + 5)}^{2}$

Rewrite the expression.

${(x^{2} + 49)}^{1} = {(x + 5)}^{2}$

Simplify.

$x^{2} + 49 = {(x + 5)}^{2}$

Solve for $x$ .

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Simplify ${(x + 5)}^{2}$ .

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Rewrite ${(x + 5)}^{2}$ as $(x + 5) (x + 5)$ .

$x^{2} + 49 = (x + 5) (x + 5)$

Expand $(x + 5) (x + 5)$ using the FOIL Method.

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Apply the distributive property.

$x^{2} + 49 = x (x + 5) + 5 (x + 5)$

Apply the distributive property.

$x^{2} + 49 = x \cdot x + x \cdot 5 + 5 (x + 5)$

Apply the distributive property.

$x^{2} + 49 = x \cdot x + x \cdot 5 + 5 x + 5 \cdot 5$

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

$x^{2} + 49 = x^{2} + x \cdot 5 + 5 x + 5 \cdot 5$

Move $5$ to the left of $x$ .

$x^{2} + 49 = x^{2} + 5 \cdot x + 5 x + 5 \cdot 5$

Multiply $5$ by $5$ .

$x^{2} + 49 = x^{2} + 5 x + 5 x + 25$

Add $5 x$ and $5 x$ .

$x^{2} + 49 = x^{2} + 10 x + 25$

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

$x^{2} + 10 x + 25 = x^{2} + 49$

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

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

$x^{2} + 10 x + 25 - x^{2} = 49$

Combine the opposite terms in $x^{2} + 10 x + 25 - x^{2}$ .

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

$10 x + 25 + 0 = 49$

Add $10 x + 25$ and $0$ .

$10 x + 25 = 49$

Move all terms not containing $x$ to the right side of the equation.

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Subtract $25$ from both sides of the equation.

$10 x = 49 - 25$

Subtract $25$ from $49$ .

$10 x = 24$

Divide each term by $10$ and simplify.

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Divide each term in $10 x = 24$ by $10$ .

$\frac{10 x}{10} = \frac{24}{10}$

Cancel the common factor of $10$ .

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Cancel the common factor.

$\frac{10 x}{10} = \frac{24}{10}$

Divide $x$ by $1$ .

$x = \frac{24}{10}$

Cancel the common factor of $24$ and $10$ .

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Factor $2$ out of $24$ .

$x = \frac{2 (12)}{10}$

Cancel the common factors.

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Factor $2$ out of $10$ .

$x = \frac{2 \cdot 12}{2 \cdot 5}$

Cancel the common factor.

$x = \frac{2 \cdot 12}{2 \cdot 5}$

Rewrite the expression.

$x = \frac{12}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{12}{5}$

Decimal Form:

$x = 2.4$

Mixed Number Form:

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

Solve for x square root of x^2+49=x+5