Solve x^2-x-1/4 - ScanMath

Question

Factor the expression

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

Show Solution

x_{1} = \frac{1 - 2}{2}, x_{2} = \frac{1 + 2}{2}

Alternative Form

x_{1} \approx - 0.207107, x_{2} \approx 1.207107

Evaluate

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

To find the roots of the expression,set the expression equal to 0

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

Multiply both sides

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

Calculate

4 x^{2} - 4 x - 1 = 0

Substitute a= 4,b= - 4 and c= - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

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

Simplify the expression

x = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 4 ( - 1 )}{8}

Simplify the expression

More Steps

x = \frac{4 \pm 32}{8}

Simplify the radical expression

More Steps

x = \frac{4 \pm 4 2}{8}

Separate the equation into 2 possible cases

x = \frac{4 + 4 2}{8} x = \frac{4 - 4 2}{8}

Simplify the expression

More Steps

x = \frac{1 + 2}{2} x = \frac{4 - 4 2}{8}

Simplify the expression

More Steps

x = \frac{1 + 2}{2} x = \frac{1 - 2}{2}

Solution

x_{1} = \frac{1 - 2}{2}, x_{2} = \frac{1 + 2}{2}

Alternative Form

x_{1} \approx - 0.207107, x_{2} \approx 1.207107

Show Solution