Solve 4x^2-17x-42

Question

Factor the expression

(x - 6) (4 x + 7)

Evaluate

4 x^{2} - 17 x - 42

Rewrite the expression

4 x^{2} + (7 - 24) x - 42

Calculate

4 x^{2} + 7 x - 24 x - 42

Rewrite the expression

x \times 4 x + x \times 7 - 6 \times 4 x - 6 \times 7

Factor out x from the expression

x (4 x + 7) - 6 \times 4 x - 6 \times 7

Factor out - 6 from the expression

x (4 x + 7) - 6 (4 x + 7)

Solution

(x - 6) (4 x + 7)

Show Solution

x_{1} = - \frac{7}{4}, x_{2} = 6

Alternative Form

x_{1} = - 1.75, x_{2} = 6

Evaluate

4 x^{2} - 17 x - 42

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

4 x^{2} - 17 x - 42 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 17 x - 42

Rewrite the expression

4 x^{2} + (7 - 24) x - 42

Calculate

4 x^{2} + 7 x - 24 x - 42

Rewrite the expression

x \times 4 x + x \times 7 - 6 \times 4 x - 6 \times 7

Factor out x from the expression

x (4 x + 7) - 6 \times 4 x - 6 \times 7

Factor out - 6 from the expression

x (4 x + 7) - 6 (4 x + 7)

Factor out 4 x + 7 from the expression

(x - 6) (4 x + 7)

(x - 6) (4 x + 7) = 0

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

x - 6 = 0 4 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

x - 6 = 0

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

x = 0 + 6

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

x = 6

x = 6 4 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

4 x + 7 = 0

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

4 x = 0 - 7

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

4 x = - 7

Divide both sides

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

Divide the numbers

x = \frac{- 7}{4}

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

x = - \frac{7}{4}

x = 6 x = - \frac{7}{4}

Solution

x_{1} = - \frac{7}{4}, x_{2} = 6

Alternative Form

x_{1} = - 1.75, x_{2} = 6

Show Solution