Solve 6x^2+17x+5 - ScanMath

Question

Factor the expression

(2 x + 5) (3 x + 1)

Evaluate

6 x^{2} + 17 x + 5

Rewrite the expression

6 x^{2} + (2 + 15) x + 5

Calculate

6 x^{2} + 2 x + 15 x + 5

Rewrite the expression

2 x \times 3 x + 2 x + 5 \times 3 x + 5

Factor out 2 x from the expression

2 x (3 x + 1) + 5 \times 3 x + 5

Factor out 5 from the expression

2 x (3 x + 1) + 5 (3 x + 1)

Solution

(2 x + 5) (3 x + 1)

Show Solution

x_{1} = - \frac{5}{2}, x_{2} = - \frac{1}{3}

Alternative Form

x_{1} = - 2.5, x_{2} = - 0. \dot{3}

Evaluate

6 x^{2} + 17 x + 5

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

6 x^{2} + 17 x + 5 = 0

Factor the expression

More Steps

Evaluate

6 x^{2} + 17 x + 5

Rewrite the expression

6 x^{2} + (2 + 15) x + 5

Calculate

6 x^{2} + 2 x + 15 x + 5

Rewrite the expression

2 x \times 3 x + 2 x + 5 \times 3 x + 5

Factor out 2 x from the expression

2 x (3 x + 1) + 5 \times 3 x + 5

Factor out 5 from the expression

2 x (3 x + 1) + 5 (3 x + 1)

Factor out 3 x + 1 from the expression

(2 x + 5) (3 x + 1)

(2 x + 5) (3 x + 1) = 0

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

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

Solve the equation for x

More Steps

Evaluate

3 x + 1 = 0

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

3 x = 0 - 1

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

3 x = - 1

Divide both sides

\frac{3 x}{3} = \frac{- 1}{3}

Divide the numbers

x = \frac{- 1}{3}

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

x = - \frac{1}{3}

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

Solution

x_{1} = - \frac{5}{2}, x_{2} = - \frac{1}{3}

Alternative Form

x_{1} = - 2.5, x_{2} = - 0. \dot{3}

Show Solution