Solve 3(20-x)^2=x^2

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 30 - 103, x_{2} = 30 + 103

Alternative Form

x_{1} \approx 12.679492, x_{2} \approx 47.320508

Evaluate

3 (20 - x)^{2} = x^{2}

Expand the expression

More Steps

1200 - 120 x + 3 x^{2} = x^{2}

Move the expression to the left side

1200 - 120 x + 2 x^{2} = 0

Rewrite in standard form

2 x^{2} - 120 x + 1200 = 0

Substitute a= 2,b= - 120 and c= 1200 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{120 \pm ( - 120 ) ^{2} - 4 \times 2 \times 1200}{2 \times 2}

Simplify the expression

x = \frac{120 \pm ( - 120 ) ^{2} - 4 \times 2 \times 1200}{4}

Simplify the expression

More Steps

x = \frac{120 \pm 4800}{4}

Simplify the radical expression

More Steps

x = \frac{120 \pm 40 3}{4}

Separate the equation into 2 possible cases

x = \frac{120 + 40 3}{4} x = \frac{120 - 40 3}{4}

Simplify the expression

More Steps

x = 30 + 103 x = \frac{120 - 40 3}{4}

Simplify the expression

More Steps

x = 30 + 103 x = 30 - 103

Solution

x_{1} = 30 - 103, x_{2} = 30 + 103

Alternative Form

x_{1} \approx 12.679492, x_{2} \approx 47.320508

Show Solution