Solve 4x^2 +23x-35

Question

Factor the expression

(x + 7) (4 x - 5)

Evaluate

4 x^{2} + 23 x - 35

Rewrite the expression

4 x^{2} + (- 5 + 28) x - 35

Calculate

4 x^{2} - 5 x + 28 x - 35

Rewrite the expression

x \times 4 x - x \times 5 + 7 \times 4 x - 7 \times 5

Factor out x from the expression

x (4 x - 5) + 7 \times 4 x - 7 \times 5

Factor out 7 from the expression

x (4 x - 5) + 7 (4 x - 5)

Solution

(x + 7) (4 x - 5)

Show Solution

x_{1} = - 7, x_{2} = \frac{5}{4}

Alternative Form

x_{1} = - 7, x_{2} = 1.25

Evaluate

4 x^{2} + 23 x - 35

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

4 x^{2} + 23 x - 35 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} + 23 x - 35

Rewrite the expression

4 x^{2} + (- 5 + 28) x - 35

Calculate

4 x^{2} - 5 x + 28 x - 35

Rewrite the expression

x \times 4 x - x \times 5 + 7 \times 4 x - 7 \times 5

Factor out x from the expression

x (4 x - 5) + 7 \times 4 x - 7 \times 5

Factor out 7 from the expression

x (4 x - 5) + 7 (4 x - 5)

Factor out 4 x - 5 from the expression

(x + 7) (4 x - 5)

(x + 7) (4 x - 5) = 0

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

x + 7 = 0 4 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

x + 7 = 0

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

x = 0 - 7

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

x = - 7

x = - 7 4 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

4 x - 5 = 0

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

4 x = 0 + 5

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

4 x = 5

Divide both sides

\frac{4 x}{4} = \frac{5}{4}

Divide the numbers

x = \frac{5}{4}

x = - 7 x = \frac{5}{4}

Solution

x_{1} = - 7, x_{2} = \frac{5}{4}

Alternative Form

x_{1} = - 7, x_{2} = 1.25

Show Solution