Solve ( 2x^2 - 3 ) - 64x = 0

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{32 - 1030}{2}, x_{2} = \frac{32 + 1030}{2}

Alternative Form

x_{1} \approx - 0.046807, x_{2} \approx 32.046807

Evaluate

(2 x^{2} - 3) - 64 x = 0

Remove the parentheses

2 x^{2} - 3 - 64 x = 0

Rewrite in standard form

2 x^{2} - 64 x - 3 = 0

Substitute a= 2,b= - 64 and c= - 3 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{64 \pm ( - 64 ) ^{2} - 4 \times 2 ( - 3 )}{2 \times 2}

Simplify the expression

x = \frac{64 \pm ( - 64 ) ^{2} - 4 \times 2 ( - 3 )}{4}

Simplify the expression

More Steps

x = \frac{64 \pm 4120}{4}

Simplify the radical expression

More Steps

x = \frac{64 \pm 2 1030}{4}

Separate the equation into 2 possible cases

x = \frac{64 + 2 1030}{4} x = \frac{64 - 2 1030}{4}

Simplify the expression

More Steps

x = \frac{32 + 1030}{2} x = \frac{64 - 2 1030}{4}

Simplify the expression

More Steps

x = \frac{32 + 1030}{2} x = \frac{32 - 1030}{2}

Solution

x_{1} = \frac{32 - 1030}{2}, x_{2} = \frac{32 + 1030}{2}

Alternative Form

x_{1} \approx - 0.046807, x_{2} \approx 32.046807

Show Solution