Solve 2(x 8)^( 1/2 )-6=-2

Evaluate

2 (x \times 8)^{\frac{1}{2}} - 6 = - 2

Find the domain

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2 (x \times 8)^{\frac{1}{2}} - 6 = - 2, x \geq 0

Simplify

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42 \times x^{\frac{1}{2}} - 6 = - 2

Move the constant to the right-hand side and change its sign

42 \times x^{\frac{1}{2}} = - 2 + 6

Add the numbers

42 \times x^{\frac{1}{2}} = 4

Divide both sides

\frac{4 2 \times x ^{\frac{1}{2}}}{4 2} = \frac{4}{4 2}

Divide the numbers

x^{\frac{1}{2}} = \frac{4}{4 2}

Divide the numbers

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

Raise both sides of the equation to the 2 -th power to eliminate the isolated 2 -th root

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

Evaluate the power

x = \frac{1}{2}

Check if the solution is in the defined range

x = \frac{1}{2}, x \geq 0

Find the intersection of the solution and the defined range

x = \frac{1}{2}

Solution

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x = \frac{1}{2}

Alternative Form

x = 0.5

Solve the equation