Solve 2x^2+9x+10 - ScanMath

Question

Factor the expression

Factor

(x + 2) (2 x + 5)

Evaluate

2 x^{2} + 9 x + 10

Rewrite the expression

2 x^{2} + (5 + 4) x + 10

Calculate

2 x^{2} + 5 x + 4 x + 10

Rewrite the expression

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

Factor out x from the expression

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

Factor out 2 from the expression

x (2 x + 5) + 2 (2 x + 5)

Solution

(x + 2) (2 x + 5)

Show Solution

Find the roots of the algebra expression

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

Alternative Form

x_{1} = - 2.5, x_{2} = - 2

Evaluate

2 x^{2} + 9 x + 10

To find the roots of the expression,set the expression equal to 0

2 x^{2} + 9 x + 10 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} + 9 x + 10

Rewrite the expression

2 x^{2} + (5 + 4) x + 10

Calculate

2 x^{2} + 5 x + 4 x + 10

Rewrite the expression

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

Factor out x from the expression

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

Factor out 2 from the expression

x (2 x + 5) + 2 (2 x + 5)

Factor out 2 x + 5 from the expression

(x + 2) (2 x + 5)

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

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

x + 2 = 0 2 x + 5 = 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 = - 2 2 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 5 = 0

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

2 x = 0 - 5

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

2 x = - 5

Divide both sides

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

Divide the numbers

x = \frac{- 5}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{5}{2}

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

Solution

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

Alternative Form

x_{1} = - 2.5, x_{2} = - 2

Show Solution