Solve 4x^2=(3-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} = - \frac{3 + 3 3}{2}, x_{2} = \frac{- 3 + 3 3}{2}

Alternative Form

x_{1} \approx - 4.098076, x_{2} \approx 1.098076

Evaluate

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

Expand the expression

More Steps

4 x^{2} = 9 - 6 x + 2 x^{2}

Move the expression to the left side

2 x^{2} - 9 + 6 x = 0

Rewrite in standard form

2 x^{2} + 6 x - 9 = 0

Substitute a= 2,b= 6 and c= - 9 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 6 \pm 6 ^{2} - 4 \times 2 ( - 9 )}{2 \times 2}

Simplify the expression

x = \frac{- 6 \pm 6 ^{2} - 4 \times 2 ( - 9 )}{4}

Simplify the expression

More Steps

x = \frac{- 6 \pm 108}{4}

Simplify the radical expression

More Steps

x = \frac{- 6 \pm 6 3}{4}

Separate the equation into 2 possible cases

x = \frac{- 6 + 6 3}{4} x = \frac{- 6 - 6 3}{4}

Simplify the expression

More Steps

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

Simplify the expression

More Steps

x = \frac{- 3 + 3 3}{2} x = - \frac{3 + 3 3}{2}

Solution

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

Alternative Form

x_{1} \approx - 4.098076, x_{2} \approx 1.098076

Show Solution