Solve 5 - (x -1)(x 1) = (x^2)2

Evaluate

5 - (x - 1) (x \times 1) = x^{2} \times 2

Remove the parentheses

5 - (x - 1) x \times 1 = x^{2} \times 2

Multiply the terms

More Steps

5 - x (x - 1) = x^{2} \times 2

Use the commutative property to reorder the terms

5 - x (x - 1) = 2 x^{2}

Expand the expression

More Steps

5 - x^{2} + x = 2 x^{2}

Move the expression to the left side

5 - 3 x^{2} + x = 0

Rewrite in standard form

- 3 x^{2} + x + 5 = 0

Multiply both sides

3 x^{2} - x - 5 = 0

Substitute a= 3,b= - 1 and c= - 5 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 3 ( - 5 )}{2 \times 3}

Simplify the expression

x = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 3 ( - 5 )}{6}

Simplify the expression

More Steps

x = \frac{1 \pm 61}{6}

Separate the equation into 2 possible cases

x = \frac{1 + 61}{6} x = \frac{1 - 61}{6}

Solution

x_{1} = \frac{1 - 61}{6}, x_{2} = \frac{1 + 61}{6}

Alternative Form

x_{1} \approx - 1.135042, x_{2} \approx 1.468375

Solve the quadratic equation