Solve (2a^2-3a 1)-(7a^2-5a)

Question

Simplify the expression

- 5 a^{2} + 2 a

Evaluate

(2 a^{2} - 3 a \times 1) - (7 a^{2} - 5 a)

Multiply the terms

(2 a^{2} - 3 a) - (7 a^{2} - 5 a)

Remove the parentheses

2 a^{2} - 3 a - (7 a^{2} - 5 a)

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

2 a^{2} - 3 a - 7 a^{2} + 5 a

Subtract the terms

More Steps

Evaluate

2 a^{2} - 7 a^{2}

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

(2 - 7) a^{2}

Subtract the numbers

- 5 a^{2}

- 5 a^{2} - 3 a + 5 a

Solution

More Steps

Evaluate

- 3 a + 5 a

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

(- 3 + 5) a

Add the numbers

2 a

- 5 a^{2} + 2 a

Show Solution

Factor the expression

- a (5 a - 2)

Evaluate

(2 a^{2} - 3 a \times 1) - (7 a^{2} - 5 a)

Multiply the terms

(2 a^{2} - 3 a) - (7 a^{2} - 5 a)

Remove the parentheses

2 a^{2} - 3 a - (7 a^{2} - 5 a)

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

2 a^{2} - 3 a - 7 a^{2} + 5 a

Subtract the terms

More Steps

Evaluate

2 a^{2} - 7 a^{2}

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

(2 - 7) a^{2}

Subtract the numbers

- 5 a^{2}

- 5 a^{2} - 3 a + 5 a

Add the terms

More Steps

Evaluate

- 3 a + 5 a

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

(- 3 + 5) a

Add the numbers

2 a

- 5 a^{2} + 2 a

Rewrite the expression

- a \times 5 a + a \times 2

Solution

- a (5 a - 2)

Show Solution

Find the roots

a_{1} = 0, a_{2} = \frac{2}{5}

Alternative Form

a_{1} = 0, a_{2} = 0.4

Evaluate

(2 a^{2} - 3 a \times 1) - (7 a^{2} - 5 a)

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

(2 a^{2} - 3 a \times 1) - (7 a^{2} - 5 a) = 0

Multiply the terms

(2 a^{2} - 3 a) - (7 a^{2} - 5 a) = 0

Remove the parentheses

2 a^{2} - 3 a - (7 a^{2} - 5 a) = 0

Subtract the terms

More Steps

Simplify

2 a^{2} - 3 a - (7 a^{2} - 5 a)

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

2 a^{2} - 3 a - 7 a^{2} + 5 a

Subtract the terms

More Steps

Evaluate

2 a^{2} - 7 a^{2}

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

(2 - 7) a^{2}

Subtract the numbers

- 5 a^{2}

- 5 a^{2} - 3 a + 5 a

Add the terms

More Steps

Evaluate

- 3 a + 5 a

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

(- 3 + 5) a

Add the numbers

2 a

- 5 a^{2} + 2 a

- 5 a^{2} + 2 a = 0

Factor the expression

More Steps

Evaluate

- 5 a^{2} + 2 a

Rewrite the expression

- a \times 5 a + a \times 2

Factor out - a from the expression

- a (5 a - 2)

- a (5 a - 2) = 0

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

- a = 0 5 a - 2 = 0

Solve the equation for a

a = 0 5 a - 2 = 0

Solve the equation for a

More Steps

Evaluate

5 a - 2 = 0

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

5 a = 0 + 2

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

5 a = 2

Divide both sides

\frac{5 a}{5} = \frac{2}{5}

Divide the numbers

a = \frac{2}{5}

a = 0 a = \frac{2}{5}

Solution

a_{1} = 0, a_{2} = \frac{2}{5}

Alternative Form

a_{1} = 0, a_{2} = 0.4

Show Solution