Solve x(2x-3)+x(7x+8)

Question

Simplify the expression

9 x^{2} + 5 x

Evaluate

x (2 x - 3) + x (7 x + 8)

Expand the expression

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Calculate

x (2 x - 3)

Apply the distributive property

x \times 2 x - x \times 3

Multiply the terms

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Evaluate

x \times 2 x

Use the commutative property to reorder the terms

2 x \times x

Multiply the terms

2 x^{2}

2 x^{2} - x \times 3

Use the commutative property to reorder the terms

2 x^{2} - 3 x

2 x^{2} - 3 x + x (7 x + 8)

Expand the expression

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Calculate

x (7 x + 8)

Apply the distributive property

x \times 7 x + x \times 8

Multiply the terms

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Evaluate

x \times 7 x

Use the commutative property to reorder the terms

7 x \times x

Multiply the terms

7 x^{2}

7 x^{2} + x \times 8

Use the commutative property to reorder the terms

7 x^{2} + 8 x

2 x^{2} - 3 x + 7 x^{2} + 8 x

Add the terms

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Evaluate

2 x^{2} + 7 x^{2}

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

(2 + 7) x^{2}

Add the numbers

9 x^{2}

9 x^{2} - 3 x + 8 x

Solution

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Evaluate

- 3 x + 8 x

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

(- 3 + 8) x

Add the numbers

5 x

9 x^{2} + 5 x

Show Solution

Factor the expression

x (9 x + 5)

Evaluate

x (2 x - 3) + x (7 x + 8)

Factor out x from the expression

x (2 x - 3 + 7 x + 8)

Solution

x (9 x + 5)

Show Solution

Find the roots

x_{1} = - \frac{5}{9}, x_{2} = 0

Alternative Form

x_{1} = - 0. \dot{5}, x_{2} = 0

Evaluate

x (2 x - 3) + x (7 x + 8)

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

x (2 x - 3) + x (7 x + 8) = 0

Calculate

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Evaluate

x (2 x - 3) + x (7 x + 8)

Expand the expression

More Steps

Calculate

x (2 x - 3)

Apply the distributive property

x \times 2 x - x \times 3

Multiply the terms

2 x^{2} - x \times 3

Use the commutative property to reorder the terms

2 x^{2} - 3 x

2 x^{2} - 3 x + x (7 x + 8)

Expand the expression

More Steps

Calculate

x (7 x + 8)

Apply the distributive property

x \times 7 x + x \times 8

Multiply the terms

7 x^{2} + x \times 8

Use the commutative property to reorder the terms

7 x^{2} + 8 x

2 x^{2} - 3 x + 7 x^{2} + 8 x

Add the terms

More Steps

Evaluate

2 x^{2} + 7 x^{2}

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

(2 + 7) x^{2}

Add the numbers

9 x^{2}

9 x^{2} - 3 x + 8 x

Add the terms

More Steps

Evaluate

- 3 x + 8 x

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

(- 3 + 8) x

Add the numbers

5 x

9 x^{2} + 5 x

9 x^{2} + 5 x = 0

Factor the expression

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Evaluate

9 x^{2} + 5 x

Rewrite the expression

x \times 9 x + x \times 5

Factor out x from the expression

x (9 x + 5)

x (9 x + 5) = 0

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

x = 0 9 x + 5 = 0

Solve the equation for x

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Evaluate

9 x + 5 = 0

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

9 x = 0 - 5

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

9 x = - 5

Divide both sides

\frac{9 x}{9} = \frac{- 5}{9}

Divide the numbers

x = \frac{- 5}{9}

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

x = - \frac{5}{9}

x = 0 x = - \frac{5}{9}

Solution

x_{1} = - \frac{5}{9}, x_{2} = 0

Alternative Form

x_{1} = - 0. \dot{5}, x_{2} = 0

Show Solution