Solve 3(- 1/3 x 1/2 ) 2x=-1-(6x- 1/2 )

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{6 - 38}{2}, x_{2} = \frac{6 + 38}{2}

Alternative Form

x_{1} \approx - 0.082207, x_{2} \approx 6.082207

Evaluate

3 (- \frac{1}{3} x \times \frac{1}{2}) \times 2 x = - 1 - (6 x - \frac{1}{2})

Simplify

More Steps

- x^{2} = - 1 - (6 x - \frac{1}{2})

Subtract the terms

More Steps

- x^{2} = - \frac{1}{2} - 6 x

Move the expression to the left side

- x^{2} + \frac{1}{2} + 6 x = 0

Rewrite in standard form

- x^{2} + 6 x + \frac{1}{2} = 0

Multiply both sides

x^{2} - 6 x - \frac{1}{2} = 0

Multiply both sides

2 (x^{2} - 6 x - \frac{1}{2}) = 2 \times 0

Calculate

2 x^{2} - 12 x - 1 = 0

Substitute a= 2,b= - 12 and c= - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 2 ( - 1 )}{2 \times 2}

Simplify the expression

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 2 ( - 1 )}{4}

Simplify the expression

More Steps

x = \frac{12 \pm 152}{4}

Simplify the radical expression

More Steps

x = \frac{12 \pm 2 38}{4}

Separate the equation into 2 possible cases

x = \frac{12 + 2 38}{4} x = \frac{12 - 2 38}{4}

Simplify the expression

More Steps

x = \frac{6 + 38}{2} x = \frac{12 - 2 38}{4}

Simplify the expression

More Steps

x = \frac{6 + 38}{2} x = \frac{6 - 38}{2}

Solution

x_{1} = \frac{6 - 38}{2}, x_{2} = \frac{6 + 38}{2}

Alternative Form

x_{1} \approx - 0.082207, x_{2} \approx 6.082207

Show Solution