Basic Math Examples

$18 - 3 y^{\frac{1}{2}} = 25$

Step 1

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

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Step 1.1

Subtract $18$ from both sides of the equation.

$- 3 y^{\frac{1}{2}} - 25 = - 18$

Step 1.2

Add $25$ to both sides of the equation.

$- 3 y^{\frac{1}{2}} = - 18 + 25$

Step 1.3

Add $- 18$ and $25$ .

$- 3 y^{\frac{1}{2}} = 7$

Step 2

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

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

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify ${(- 3 y^{\frac{1}{2}})}^{2}$ .

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Step 3.1.1.1

Apply the product rule to $- 3 y^{\frac{1}{2}}$ .

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

Step 3.1.1.2

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

$9 {(y^{\frac{1}{2}})}^{2} = 7^{2}$

Step 3.1.1.3

Multiply the exponents in ${(y^{\frac{1}{2}})}^{2}$ .

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Step 3.1.1.3.1

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

$9 y^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 3.1.1.3.2

Cancel the common factor of $2$ .

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Step 3.1.1.3.2.1

Cancel the common factor.

$9 y^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 3.1.1.3.2.2

Rewrite the expression.

$9 y^{1} = 7^{2}$

Step 3.1.1.4

Simplify.

$9 y = 7^{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Raise $7$ to the power of $2$ .

$9 y = 49$

Step 4

Divide each term in $9 y = 49$ by $9$ and simplify.

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Step 4.1

Divide each term in $9 y = 49$ by $9$ .

$\frac{9 y}{9} = \frac{49}{9}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $9$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{49}{9}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{49}{9}$

Step 5

Exclude the solutions that do not make $18 - 3 y^{\frac{1}{2}} = 25$ true.

$No solution$