Solve x^2-3x \sqrt 3-x=\sqrt 3-x 10

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = - 5 - 25 + 3, x_{2} = - 5 + 25 + 3

Alternative Form

x_{1} \approx - 10.170305, x_{2} \approx 0.170305

Evaluate

x^{2} - 3 x 3 - x = 3 - x \times 10

Calculate the product

x^{2} - 33 \times x - x = 3 - x \times 10

Use the commutative property to reorder the terms

x^{2} - 33 \times x - x = 3 - 10 x

Move the expression to the left side

x^{2} - 33 \times x + 9 x - 3 = 0

Substitute a= 1,b= 10 and c= - 3 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 10 \pm 1 0 ^{2} - 4 ( - 3 )}{2}

Simplify the expression

More Steps

x = \frac{- 10 \pm 100 + 4 3}{2}

Simplify the radical expression

More Steps

x = \frac{- 10 \pm 2 25 + 3}{2}

Separate the equation into 2 possible cases

x = \frac{- 10 + 2 25 + 3}{2} x = \frac{- 10 - 2 25 + 3}{2}

Simplify the expression

More Steps

x = - 5 + 25 + 3 x = \frac{- 10 - 2 25 + 3}{2}

Simplify the expression

More Steps

x = - 5 + 25 + 3 x = - 5 - 25 + 3

Solution

x_{1} = - 5 - 25 + 3, x_{2} = - 5 + 25 + 3

Alternative Form

x_{1} \approx - 10.170305, x_{2} \approx 0.170305

Show Solution