Solve (40x^2-6x^2)-(21x^2-10x 8)

Question

Simplify the expression

13 x^{2} + 80 x

Evaluate

(40 x^{2} - 6 x^{2}) - (21 x^{2} - 10 x \times 8)

Subtract the terms

More Steps

Simplify

40 x^{2} - 6 x^{2}

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

(40 - 6) x^{2}

Subtract the numbers

34 x^{2}

34 x^{2} - (21 x^{2} - 10 x \times 8)

Multiply the terms

34 x^{2} - (21 x^{2} - 80 x)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

34 x^{2} - 21 x^{2} + 80 x

Solution

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Evaluate

34 x^{2} - 21 x^{2}

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

(34 - 21) x^{2}

Subtract the numbers

13 x^{2}

13 x^{2} + 80 x

Show Solution

Factor the expression

x (13 x + 80)

Evaluate

(40 x^{2} - 6 x^{2}) - (21 x^{2} - 10 x \times 8)

Subtract the terms

More Steps

Simplify

40 x^{2} - 6 x^{2}

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

(40 - 6) x^{2}

Subtract the numbers

34 x^{2}

34 x^{2} - (21 x^{2} - 10 x \times 8)

Multiply the terms

34 x^{2} - (21 x^{2} - 80 x)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

34 x^{2} - 21 x^{2} + 80 x

Subtract the terms

More Steps

Evaluate

34 x^{2} - 21 x^{2}

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

(34 - 21) x^{2}

Subtract the numbers

13 x^{2}

13 x^{2} + 80 x

Rewrite the expression

x \times 13 x + x \times 80

Solution

x (13 x + 80)

Show Solution

Find the roots

x_{1} = - \frac{80}{13}, x_{2} = 0

Alternative Form

x_{1} = - 6. \dot{1} 5384 \dot{6}, x_{2} = 0

Evaluate

(40 x^{2} - 6 x^{2}) - (21 x^{2} - 10 x \times 8)

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

(40 x^{2} - 6 x^{2}) - (21 x^{2} - 10 x \times 8) = 0

Subtract the terms

More Steps

Simplify

40 x^{2} - 6 x^{2}

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

(40 - 6) x^{2}

Subtract the numbers

34 x^{2}

34 x^{2} - (21 x^{2} - 10 x \times 8) = 0

Multiply the terms

34 x^{2} - (21 x^{2} - 80 x) = 0

Subtract the terms

More Steps

Simplify

34 x^{2} - (21 x^{2} - 80 x)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

34 x^{2} - 21 x^{2} + 80 x

Subtract the terms

More Steps

Evaluate

34 x^{2} - 21 x^{2}

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

(34 - 21) x^{2}

Subtract the numbers

13 x^{2}

13 x^{2} + 80 x

13 x^{2} + 80 x = 0

Factor the expression

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Evaluate

13 x^{2} + 80 x

Rewrite the expression

x \times 13 x + x \times 80

Factor out x from the expression

x (13 x + 80)

x (13 x + 80) = 0

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

x = 0 13 x + 80 = 0

Solve the equation for x

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Evaluate

13 x + 80 = 0

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

13 x = 0 - 80

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

13 x = - 80

Divide both sides

\frac{13 x}{13} = \frac{- 80}{13}

Divide the numbers

x = \frac{- 80}{13}

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

x = - \frac{80}{13}

x = 0 x = - \frac{80}{13}

Solution

x_{1} = - \frac{80}{13}, x_{2} = 0

Alternative Form

x_{1} = - 6. \dot{1} 5384 \dot{6}, x_{2} = 0

Show Solution