Basic Math Examples

$s - 7 = \sqrt{14 s + 49}$

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.

$\sqrt{14 s + 49} = s - 7$

Step 2

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

${\sqrt{14 s + 49}}^{2} = {(s - 7)}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{14 s + 49}$ as ${(14 s + 49)}^{\frac{1}{2}}$ .

${({(14 s + 49)}^{\frac{1}{2}})}^{2} = {(s - 7)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(14 s + 49)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(14 s + 49)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(14 s + 49)}^{\frac{1}{2} \cdot 2} = {(s - 7)}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(14 s + 49)}^{\frac{1}{2} \cdot 2} = {(s - 7)}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(14 s + 49)}^{1} = {(s - 7)}^{2}$

Step 3.2.1.2

Simplify.

$14 s + 49 = {(s - 7)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(s - 7)}^{2}$ .

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Step 3.3.1.1

Rewrite ${(s - 7)}^{2}$ as $(s - 7) (s - 7)$ .

$14 s + 49 = (s - 7) (s - 7)$

Step 3.3.1.2

Expand $(s - 7) (s - 7)$ using the FOIL Method.

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Step 3.3.1.2.1

Apply the distributive property.

$14 s + 49 = s (s - 7) - 7 (s - 7)$

Step 3.3.1.2.2

Apply the distributive property.

$14 s + 49 = s \cdot s + s \cdot - 7 - 7 (s - 7)$

Step 3.3.1.2.3

Apply the distributive property.

$14 s + 49 = s \cdot s + s \cdot - 7 - 7 s - 7 \cdot - 7$

Step 3.3.1.3

Simplify and combine like terms.

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Step 3.3.1.3.1

Simplify each term.

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Step 3.3.1.3.1.1

Multiply $s$ by $s$ .

$14 s + 49 = s^{2} + s \cdot - 7 - 7 s - 7 \cdot - 7$

Step 3.3.1.3.1.2

Move $- 7$ to the left of $s$ .

$14 s + 49 = s^{2} - 7 \cdot s - 7 s - 7 \cdot - 7$

Step 3.3.1.3.1.3

Multiply $- 7$ by $- 7$ .

$14 s + 49 = s^{2} - 7 s - 7 s + 49$

Step 3.3.1.3.2

Subtract $7 s$ from $- 7 s$ .

$14 s + 49 = s^{2} - 14 s + 49$

Step 4

Solve for $s$ .

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Step 4.1

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

$s^{2} - 14 s + 49 = 14 s + 49$

Step 4.2

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

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Step 4.2.1

Subtract $14 s$ from both sides of the equation.

$s^{2} - 14 s + 49 - 14 s = 49$

Step 4.2.2

Subtract $14 s$ from $- 14 s$ .

$s^{2} - 28 s + 49 = 49$

Step 4.3

Subtract $49$ from both sides of the equation.

$s^{2} - 28 s + 49 - 49 = 0$

Step 4.4

Combine the opposite terms in $s^{2} - 28 s + 49 - 49$ .

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Step 4.4.1

Subtract $49$ from $49$ .

$s^{2} - 28 s + 0 = 0$

Step 4.4.2

Add $s^{2} - 28 s$ and $0$ .

$s^{2} - 28 s = 0$

Step 4.5

Factor $s$ out of $s^{2} - 28 s$ .

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Step 4.5.1

Factor $s$ out of $s^{2}$ .

$s \cdot s - 28 s = 0$

Step 4.5.2

Factor $s$ out of $- 28 s$ .

$s \cdot s + s \cdot - 28 = 0$

Step 4.5.3

Factor $s$ out of $s \cdot s + s \cdot - 28$ .

$s (s - 28) = 0$

Step 4.6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$s = 0$

$s - 28 = 0$

Step 4.7

Set $s$ equal to $0$ .

$s = 0$

Step 4.8

Set $s - 28$ equal to $0$ and solve for $s$ .

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Step 4.8.1

Set $s - 28$ equal to $0$ .

$s - 28 = 0$

Step 4.8.2

Add $28$ to both sides of the equation.

$s = 28$

Step 4.9

The final solution is all the values that make $s (s - 28) = 0$ true.

$s = 0, 28$

Step 5

Exclude the solutions that do not make $s - 7 = \sqrt{14 s + 49}$ true.

$s = 28$