Solve 4x^2-22x 10-32x^2-7x

Question

Simplify the expression

- 28 x^{2} - 227 x

Evaluate

4 x^{2} - 22 x \times 10 - 32 x^{2} - 7 x

Multiply the terms

4 x^{2} - 220 x - 32 x^{2} - 7 x

Subtract the terms

More Steps

Evaluate

4 x^{2} - 32 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(4 - 32) x^{2}

Subtract the numbers

- 28 x^{2}

- 28 x^{2} - 220 x - 7 x

Solution

More Steps

Evaluate

- 220 x - 7 x

Collect like terms by calculating the sum or difference of their coefficients

(- 220 - 7) x

Subtract the numbers

- 227 x

- 28 x^{2} - 227 x

Show Solution

Factor the expression

- x (28 x + 227)

Evaluate

4 x^{2} - 22 x \times 10 - 32 x^{2} - 7 x

Multiply the terms

4 x^{2} - 220 x - 32 x^{2} - 7 x

Subtract the terms

More Steps

Simplify

4 x^{2} - 220 x - 32 x^{2}

Subtract the terms

More Steps

Evaluate

4 x^{2} - 32 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(4 - 32) x^{2}

Subtract the numbers

- 28 x^{2}

- 28 x^{2} - 220 x

- 28 x^{2} - 220 x - 7 x

Subtract the terms

More Steps

Evaluate

- 220 x - 7 x

Collect like terms by calculating the sum or difference of their coefficients

(- 220 - 7) x

Subtract the numbers

- 227 x

- 28 x^{2} - 227 x

Rewrite the expression

- x \times 28 x - x \times 227

Solution

- x (28 x + 227)

Show Solution

Find the roots

x_{1} = - \frac{227}{28}, x_{2} = 0

Alternative Form

x_{1} = - 8.10 \dot{7} 1428 \dot{5}, x_{2} = 0

Evaluate

4 x^{2} - 22 x \times 10 - 32 x^{2} - 7 x

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

4 x^{2} - 22 x \times 10 - 32 x^{2} - 7 x = 0

Multiply the terms

4 x^{2} - 220 x - 32 x^{2} - 7 x = 0

Subtract the terms

More Steps

Simplify

4 x^{2} - 220 x - 32 x^{2}

Subtract the terms

More Steps

Evaluate

4 x^{2} - 32 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(4 - 32) x^{2}

Subtract the numbers

- 28 x^{2}

- 28 x^{2} - 220 x

- 28 x^{2} - 220 x - 7 x = 0

Subtract the terms

More Steps

Simplify

- 28 x^{2} - 220 x - 7 x

Subtract the terms

More Steps

Evaluate

- 220 x - 7 x

Collect like terms by calculating the sum or difference of their coefficients

(- 220 - 7) x

Subtract the numbers

- 227 x

- 28 x^{2} - 227 x

- 28 x^{2} - 227 x = 0

Factor the expression

More Steps

Evaluate

- 28 x^{2} - 227 x

Rewrite the expression

- x \times 28 x - x \times 227

Factor out - x from the expression

- x (28 x + 227)

- x (28 x + 227) = 0

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

- x = 0 28 x + 227 = 0

Solve the equation for x

x = 0 28 x + 227 = 0

Solve the equation for x

More Steps

Evaluate

28 x + 227 = 0

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

28 x = 0 - 227

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

28 x = - 227

Divide both sides

\frac{28 x}{28} = \frac{- 227}{28}

Divide the numbers

x = \frac{- 227}{28}

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

x = - \frac{227}{28}

x = 0 x = - \frac{227}{28}

Solution

x_{1} = - \frac{227}{28}, x_{2} = 0

Alternative Form

x_{1} = - 8.10 \dot{7} 1428 \dot{5}, x_{2} = 0

Show Solution