Solve (5x-6)2 - 65x - 652 = 25 - 5x^2

Evaluate

(5 x - 6) \times 2 - 65 x - 652 = 25 - 5 x^{2}

Multiply the terms

2 (5 x - 6) - 65 x - 652 = 25 - 5 x^{2}

Swap the sides

25 - 5 x^{2} = 2 (5 x - 6) - 65 x - 652

Expand the expression

More Steps

25 - 5 x^{2} = - 55 x - 664

Move the expression to the left side

689 - 5 x^{2} + 55 x = 0

Rewrite in standard form

- 5 x^{2} + 55 x + 689 = 0

Multiply both sides

5 x^{2} - 55 x - 689 = 0

Substitute a= 5,b= - 55 and c= - 689 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{55 \pm ( - 55 ) ^{2} - 4 \times 5 ( - 689 )}{2 \times 5}

Simplify the expression

x = \frac{55 \pm ( - 55 ) ^{2} - 4 \times 5 ( - 689 )}{10}

Simplify the expression

More Steps

x = \frac{55 \pm 16805}{10}

Separate the equation into 2 possible cases

x = \frac{55 + 16805}{10} x = \frac{55 - 16805}{10}

Solution

x_{1} = \frac{55 - 16805}{10}, x_{2} = \frac{55 + 16805}{10}

Alternative Form

x_{1} \approx - 7.46341, x_{2} \approx 18.46341

Solve the quadratic equation