Solve (4x-1)3 (3-2x)3=(2x^2)3

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{21 - 3 23}{26}, x_{2} = \frac{21 + 3 23}{26}

Alternative Form

x_{1} \approx 0.254327, x_{2} \approx 1.361057

Evaluate

(4 x - 1) \times 3 (3 - 2 x) \times 3 = 2 x^{2} \times 3

Simplify

(4 x - 1) \times 3 (3 - 2 x) = 2 x^{2}

Multiply the first two terms

3 (4 x - 1) (3 - 2 x) = 2 x^{2}

Expand the expression

More Steps

42 x - 24 x^{2} - 9 = 2 x^{2}

Move the expression to the left side

42 x - 26 x^{2} - 9 = 0

Rewrite in standard form

- 26 x^{2} + 42 x - 9 = 0

Multiply both sides

26 x^{2} - 42 x + 9 = 0

Substitute a= 26,b= - 42 and c= 9 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{42 \pm ( - 42 ) ^{2} - 4 \times 26 \times 9}{2 \times 26}

Simplify the expression

x = \frac{42 \pm ( - 42 ) ^{2} - 4 \times 26 \times 9}{52}

Simplify the expression

More Steps

x = \frac{42 \pm 828}{52}

Simplify the radical expression

More Steps

x = \frac{42 \pm 6 23}{52}

Separate the equation into 2 possible cases

x = \frac{42 + 6 23}{52} x = \frac{42 - 6 23}{52}

Simplify the expression

More Steps

x = \frac{21 + 3 23}{26} x = \frac{42 - 6 23}{52}

Simplify the expression

More Steps

x = \frac{21 + 3 23}{26} x = \frac{21 - 3 23}{26}

Solution

x_{1} = \frac{21 - 3 23}{26}, x_{2} = \frac{21 + 3 23}{26}

Alternative Form

x_{1} \approx 0.254327, x_{2} \approx 1.361057

Show Solution