Solve (x-4^2) = 2x^2 -6x 13

Evaluate

x - 4^{2} = 2 x^{2} - 6 x \times 13

Evaluate the power

x - 16 = 2 x^{2} - 6 x \times 13

Multiply the terms

x - 16 = 2 x^{2} - 78 x

Swap the sides

2 x^{2} - 78 x = x - 16

Move the expression to the left side

2 x^{2} - 79 x + 16 = 0

Substitute a= 2,b= - 79 and c= 16 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{79 \pm ( - 79 ) ^{2} - 4 \times 2 \times 16}{2 \times 2}

Simplify the expression

x = \frac{79 \pm ( - 79 ) ^{2} - 4 \times 2 \times 16}{4}

Simplify the expression

More Steps

x = \frac{79 \pm 6113}{4}

Separate the equation into 2 possible cases

x = \frac{79 + 6113}{4} x = \frac{79 - 6113}{4}

Solution

x_{1} = \frac{79 - 6113}{4}, x_{2} = \frac{79 + 6113}{4}

Alternative Form

x_{1} \approx 0.203581, x_{2} \approx 39.296419

Solve the quadratic equation