Solve 3x^2+22x+7 - ScanMath

Question

Factor the expression

(x + 7) (3 x + 1)

Evaluate

3 x^{2} + 22 x + 7

Rewrite the expression

3 x^{2} + (1 + 21) x + 7

Calculate

3 x^{2} + x + 21 x + 7

Rewrite the expression

x \times 3 x + x + 7 \times 3 x + 7

Factor out x from the expression

x (3 x + 1) + 7 \times 3 x + 7

Factor out 7 from the expression

x (3 x + 1) + 7 (3 x + 1)

Solution

(x + 7) (3 x + 1)

Show Solution

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

Alternative Form

x_{1} = - 7, x_{2} = - 0. \dot{3}

Evaluate

3 x^{2} + 22 x + 7

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

3 x^{2} + 22 x + 7 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} + 22 x + 7

Rewrite the expression

3 x^{2} + (1 + 21) x + 7

Calculate

3 x^{2} + x + 21 x + 7

Rewrite the expression

x \times 3 x + x + 7 \times 3 x + 7

Factor out x from the expression

x (3 x + 1) + 7 \times 3 x + 7

Factor out 7 from the expression

x (3 x + 1) + 7 (3 x + 1)

Factor out 3 x + 1 from the expression

(x + 7) (3 x + 1)

(x + 7) (3 x + 1) = 0

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

x + 7 = 0 3 x + 1 = 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 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 = - 7 x = - \frac{1}{3}

Solution

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

Alternative Form

x_{1} = - 7, x_{2} = - 0. \dot{3}

Show Solution