Solve [1 (192x/7)]^¼ = 4x^2 2^8

Evaluate

\frac{( 1 \times ( 192 \times \frac{x}{7} ) ) ^{1}}{4} = 4 x^{2} \times 2^{8}

Remove the parentheses

\frac{( 1 \times 192 \times \frac{x}{7} ) ^{1}}{4} = 4 x^{2} \times 2^{8}

Simplify

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\frac{48 x}{7} = 4 x^{2} \times 2^{8}

Multiply

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\frac{48 x}{7} = 2^{10} x^{2}

Swap the sides

2^{10} x^{2} = \frac{48 x}{7}

Multiply both sides of the equation by LCD

2^{10} x^{2} \times 7 = \frac{48 x}{7} \times 7

Simplify the equation

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7168 x^{2} = \frac{48 x}{7} \times 7

Simplify the equation

7168 x^{2} = 48 x

Move the expression to the left side

7168 x^{2} - 48 x = 0

Factor the expression

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16 x (448 x - 3) = 0

When the product of factors equals 0,at least one factor is 0

448 x - 3 = 0 16 x = 0

Solve the equation for x

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x = \frac{3}{448} 16 x = 0

Solve the equation for x

x = \frac{3}{448} x = 0

Solution

x_{1} = 0, x_{2} = \frac{3}{448}

Alternative Form

x_{1} = 0, x_{2} \approx 0.006696

Solve the quadratic equation