Solve 4x+2x(22-x)=70

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 12 - 109, x_{2} = 12 + 109

Alternative Form

x_{1} \approx 1.559693, x_{2} \approx 22.440307

Evaluate

4 x + 2 x (22 - x) = 70

Expand the expression

More Steps

48 x - 2 x^{2} = 70

Move the expression to the left side

48 x - 2 x^{2} - 70 = 0

Rewrite in standard form

- 2 x^{2} + 48 x - 70 = 0

Multiply both sides

2 x^{2} - 48 x + 70 = 0

Substitute a= 2,b= - 48 and c= 70 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{48 \pm ( - 48 ) ^{2} - 4 \times 2 \times 70}{2 \times 2}

Simplify the expression

x = \frac{48 \pm ( - 48 ) ^{2} - 4 \times 2 \times 70}{4}

Simplify the expression

More Steps

x = \frac{48 \pm 1744}{4}

Simplify the radical expression

More Steps

x = \frac{48 \pm 4 109}{4}

Separate the equation into 2 possible cases

x = \frac{48 + 4 109}{4} x = \frac{48 - 4 109}{4}

Simplify the expression

More Steps

x = 12 + 109 x = \frac{48 - 4 109}{4}

Simplify the expression

More Steps

x = 12 + 109 x = 12 - 109

Solution

x_{1} = 12 - 109, x_{2} = 12 + 109

Alternative Form

x_{1} \approx 1.559693, x_{2} \approx 22.440307

Show Solution