Solve 2x^2 +9x+3=8

Question

Solve the quadratic equation

x_{1} = - 5, x_{2} = \frac{1}{2}

Alternative Form

x_{1} = - 5, x_{2} = 0.5

Evaluate

2 x^{2} + 9 x + 3 = 8

Move the expression to the left side

2 x^{2} + 9 x - 5 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} + 9 x - 5

Rewrite the expression

2 x^{2} + (- 1 + 10) x - 5

Calculate

2 x^{2} - x + 10 x - 5

Rewrite the expression

x \times 2 x - x + 5 \times 2 x - 5

Factor out x from the expression

x (2 x - 1) + 5 \times 2 x - 5

Factor out 5 from the expression

x (2 x - 1) + 5 (2 x - 1)

Factor out 2 x - 1 from the expression

(x + 5) (2 x - 1)

(x + 5) (2 x - 1) = 0

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

2 x - 1 = 0 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 1 = 0

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

2 x = 0 + 1

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

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = \frac{1}{2} x + 5 = 0

Solve the equation for x

More Steps

Evaluate

x + 5 = 0

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

x = 0 - 5

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

x = - 5

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

Solution

x_{1} = - 5, x_{2} = \frac{1}{2}

Alternative Form

x_{1} = - 5, x_{2} = 0.5

Show Solution