Solve by Factoring 4x^(1/2)-5=27

$4 x^{\frac{1}{2}} - 5 = 27$

Step 1

Subtract $27$ from both sides of the equation.

$4 x^{\frac{1}{2}} - 5 - 27 = 0$

Step 2

Subtract $27$ from $- 5$ .

$4 x^{\frac{1}{2}} - 32 = 0$

Step 3

Factor $4$ out of $4 x^{\frac{1}{2}} - 32$ .

Factor $4$ out of $4 x^{\frac{1}{2}}$ .

$4 (x^{\frac{1}{2}}) - 32 = 0$

Factor $4$ out of $- 32$ .

$4 x^{\frac{1}{2}} + 4 \cdot - 8 = 0$

Factor $4$ out of $4 x^{\frac{1}{2}} + 4 \cdot - 8$ .

$4 (x^{\frac{1}{2}} - 8) = 0$

Step 4

Simplify.

Apply the distributive property.

$4 x^{\frac{1}{2}} + 4 \cdot - 8 = 0$

Multiply $4$ by $- 8$ .

$4 x^{\frac{1}{2}} - 32 = 0$

Step 5

Divide each term in $(4 x^{\frac{1}{2}} - 32) = 0$ by $4$ and simplify.

Divide each term in $(4 x^{\frac{1}{2}} - 32) = 0$ by $4$ .

$\frac{(4 x^{\frac{1}{2}} - 32)}{4} = \frac{0}{4}$

Simplify the left side.

Factor $4$ out of $4 x^{\frac{1}{2}}$ .

$\frac{4 (x^{\frac{1}{2}}) - 32}{4} = \frac{0}{4}$

Factor $4$ out of $- 32$ .

$\frac{4 (x^{\frac{1}{2}}) + 4 \cdot - 8}{4} = \frac{0}{4}$

Factor $4$ out of $4 (x^{\frac{1}{2}}) + 4 (- 8)$ .

$\frac{4 (x^{\frac{1}{2}} - 8)}{4} = \frac{0}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{4 (x^{\frac{1}{2}} - 8)}{4 (1)} = \frac{0}{4}$

Cancel the common factor.

$\frac{4 (x^{\frac{1}{2}} - 8)}{4 \cdot 1} = \frac{0}{4}$

Rewrite the expression.

$\frac{x^{\frac{1}{2}} - 8}{1} = \frac{0}{4}$

Divide $x^{\frac{1}{2}} - 8$ by $1$ .

$x^{\frac{1}{2}} - 8 = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x^{\frac{1}{2}} - 8 = 0$

Step 6

Add $8$ to both sides of the equation.

$x^{\frac{1}{2}} = 8$

Step 7

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

${(x^{\frac{1}{2}})}^{2} = 8^{2}$

Step 8

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

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

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

$x^{\frac{1}{2} \cdot 2} = 8^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 8^{2}$

Rewrite the expression.

$x^{1} = 8^{2}$

Simplify.

$x = 8^{2}$

Simplify the right side.

Raise $8$ to the power of $2$ .

$x = 64$

Solve by Factoring 4x^(1/2)-5=27

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