Solve sqrt(x 2) sqrt(3-x)=3

Evaluate

x \times 2 \times 3 - x = 3

Simplify

More Steps

6 x - 2 x^{2} = 3

Raise both sides of the equation to the 2 -th power to eliminate the isolated 2 -th root

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

Evaluate the power

6 x - 2 x^{2} = 9

Move the expression to the left side

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

Rewrite in standard form

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

Multiply both sides

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 \times 9}{2 \times 2}

Simplify the expression

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

Simplify the expression

More Steps

x = \frac{6 \pm - 36}{4}

Solution

x \in / R

Alternative Form

No real solution

Solve the equation