Solve 1/2x^2-5/2x=-3

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 2, x_{2} = 3

Evaluate

\frac{1}{2} x^{2} - \frac{5}{2} x = - 3

Move the expression to the left side

\frac{1}{2} x^{2} - \frac{5}{2} x + 3 = 0

Factor the expression

More Steps

Evaluate

\frac{1}{2} x^{2} - \frac{5}{2} x + 3

Rewrite the expression

\frac{1}{2} x^{2} - \frac{1}{2} \times 5 x + \frac{1}{2} \times 6

Factor out \frac{1}{2} from the expression

\frac{1}{2} (x^{2} - 5 x + 6)

Factor the expression

More Steps

Evaluate

x^{2} - 5 x + 6

Rewrite the expression

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

Calculate

x^{2} - 2 x - 3 x + 6

Rewrite the expression

x \times x - x \times 2 - 3 x + 3 \times 2

Factor out x from the expression

x (x - 2) - 3 x + 3 \times 2

Factor out - 3 from the expression

x (x - 2) - 3 (x - 2)

Factor out x - 2 from the expression

(x - 3) (x - 2)

\frac{1}{2} (x - 3) (x - 2)

\frac{1}{2} (x - 3) (x - 2) = 0

Divide the terms

(x - 3) (x - 2) = 0

When the product of factors equals 0,at least one factor is 0

x - 3 = 0 x - 2 = 0

Solve the equation for x

More Steps

Evaluate

x - 3 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

x = 3

x = 3 x - 2 = 0

Solve the equation for x

More Steps

Evaluate

x - 2 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 2

Removing 0 doesn't change the value,so remove it from the expression

x = 2

x = 3 x = 2

Solution

x_{1} = 2, x_{2} = 3

Show Solution