Solve 1-2(2x-1)x=5x-(5-3x)

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = - \frac{3 + 33}{4}, x_{2} = \frac{- 3 + 33}{4}

Alternative Form

x_{1} \approx - 2.186141, x_{2} \approx 0.686141

Evaluate

1 - 2 (2 x - 1) x = 5 x - (5 - 3 x)

Multiply the terms

1 - 2 x (2 x - 1) = 5 x - (5 - 3 x)

Subtract the terms

More Steps

1 - 2 x (2 x - 1) = 8 x - 5

Expand the expression

More Steps

1 - 4 x^{2} + 2 x = 8 x - 5

Move the expression to the left side

6 - 4 x^{2} - 6 x = 0

Rewrite in standard form

- 4 x^{2} - 6 x + 6 = 0

Multiply both sides

4 x^{2} + 6 x - 6 = 0

Substitute a= 4,b= 6 and c= - 6 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

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

Simplify the expression

x = \frac{- 6 \pm 6 ^{2} - 4 \times 4 ( - 6 )}{8}

Simplify the expression

More Steps

x = \frac{- 6 \pm 132}{8}

Simplify the radical expression

More Steps

x = \frac{- 6 \pm 2 33}{8}

Separate the equation into 2 possible cases

x = \frac{- 6 + 2 33}{8} x = \frac{- 6 - 2 33}{8}

Simplify the expression

More Steps

x = \frac{- 3 + 33}{4} x = \frac{- 6 - 2 33}{8}

Simplify the expression

More Steps

x = \frac{- 3 + 33}{4} x = - \frac{3 + 33}{4}

Solution

x_{1} = - \frac{3 + 33}{4}, x_{2} = \frac{- 3 + 33}{4}

Alternative Form

x_{1} \approx - 2.186141, x_{2} \approx 0.686141

Show Solution