Solve 1/2 1/2x = (x^2 - 7x 10)/4x

Question

Solve the equation

x_{1} = 35 - 1226, x_{2} = 0, x_{3} = 35 + 1226

Alternative Form

x_{1} \approx - 0.014283, x_{2} = 0, x_{3} \approx 70.014283

Evaluate

\frac{1}{2} \times \frac{1}{2} x = \frac{x ^{2} - 7 x \times 10}{4} \times x

Multiply the terms

More Steps

\frac{1}{4} x = \frac{x ^{2} - 7 x \times 10}{4} \times x

Simplify

More Steps

\frac{1}{4} x = \frac{x ( x ^{2} - 70 x )}{4}

Rewrite the expression

\frac{x}{4} = \frac{x ( x ^{2} - 70 x )}{4}

Cross multiply

x \times 4 = 4 x (x^{2} - 70 x)

Simplify the equation

4 x = 4 x (x^{2} - 70 x)

Evaluate

x = x (x^{2} - 70 x)

Expand the expression

More Steps

x = x^{3} - 70 x^{2}

Move the expression to the left side

x - (x^{3} - 70 x^{2}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x - x^{3} + 70 x^{2} = 0

Factor the expression

x (1 - x^{2} + 70 x) = 0

Separate the equation into 2 possible cases

x = 0 1 - x^{2} + 70 x = 0

Solve the equation

More Steps

x = 0 x = 35 + 1226 x = 35 - 1226

Solution

x_{1} = 35 - 1226, x_{2} = 0, x_{3} = 35 + 1226

Alternative Form

x_{1} \approx - 0.014283, x_{2} = 0, x_{3} \approx 70.014283

Show Solution

Solve the equation

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