Solve 6x^2-11x-35

Question

Factor the expression

Factor

(2 x - 7) (3 x + 5)

Evaluate

6 x^{2} - 11 x - 35

Rewrite the expression

6 x^{2} + (10 - 21) x - 35

Calculate

6 x^{2} + 10 x - 21 x - 35

Rewrite the expression

2 x \times 3 x + 2 x \times 5 - 7 \times 3 x - 7 \times 5

Factor out 2 x from the expression

2 x (3 x + 5) - 7 \times 3 x - 7 \times 5

Factor out - 7 from the expression

2 x (3 x + 5) - 7 (3 x + 5)

Solution

(2 x - 7) (3 x + 5)

Show Solution

Find the roots of the algebra expression

x_{1} = - \frac{5}{3}, x_{2} = \frac{7}{2}

Alternative Form

x_{1} = - 1. \dot{6}, x_{2} = 3.5

Evaluate

6 x^{2} - 11 x - 35

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

6 x^{2} - 11 x - 35 = 0

Factor the expression

More Steps

Evaluate

6 x^{2} - 11 x - 35

Rewrite the expression

6 x^{2} + (10 - 21) x - 35

Calculate

6 x^{2} + 10 x - 21 x - 35

Rewrite the expression

2 x \times 3 x + 2 x \times 5 - 7 \times 3 x - 7 \times 5

Factor out 2 x from the expression

2 x (3 x + 5) - 7 \times 3 x - 7 \times 5

Factor out - 7 from the expression

2 x (3 x + 5) - 7 (3 x + 5)

Factor out 3 x + 5 from the expression

(2 x - 7) (3 x + 5)

(2 x - 7) (3 x + 5) = 0

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

2 x - 7 = 0 3 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 7 = 0

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

2 x = 0 + 7

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

2 x = 7

Divide both sides

\frac{2 x}{2} = \frac{7}{2}

Divide the numbers

x = \frac{7}{2}

x = \frac{7}{2} 3 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 5 = 0

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

3 x = 0 - 5

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

3 x = - 5

Divide both sides

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

Divide the numbers

x = \frac{- 5}{3}

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

x = - \frac{5}{3}

x = \frac{7}{2} x = - \frac{5}{3}

Solution

x_{1} = - \frac{5}{3}, x_{2} = \frac{7}{2}

Alternative Form

x_{1} = - 1. \dot{6}, x_{2} = 3.5

Show Solution