Solve (x^2-5)(x+5)+25

Question

Simplify the expression

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

Evaluate

(x^{2} - 5) (x + 5) + 25

Expand the expression

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Calculate

(x^{2} - 5) (x + 5)

Apply the distributive property

x^{2} \times x + x^{2} \times 5 - 5 x - 5 \times 5

Multiply the terms

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Evaluate

x^{2} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 1}

Add the numbers

x^{3}

x^{3} + x^{2} \times 5 - 5 x - 5 \times 5

Use the commutative property to reorder the terms

x^{3} + 5 x^{2} - 5 x - 5 \times 5

Multiply the numbers

x^{3} + 5 x^{2} - 5 x - 25

x^{3} + 5 x^{2} - 5 x - 25 + 25

Solution

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

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Factor the expression

x (x^{2} + 5 x - 5)

Evaluate

(x^{2} - 5) (x + 5) + 25

Simplify

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Evaluate

(x^{2} - 5) (x + 5)

Apply the distributive property

x^{2} \times x + x^{2} \times 5 - 5 x - 5 \times 5

Multiply the terms

More Steps

Evaluate

x^{2} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 1}

Add the numbers

x^{3}

x^{3} + x^{2} \times 5 - 5 x - 5 \times 5

Use the commutative property to reorder the terms

x^{3} + 5 x^{2} - 5 x - 5 \times 5

Multiply the terms

x^{3} + 5 x^{2} - 5 x - 25

x^{3} + 5 x^{2} - 5 x - 25 + 25

Since two opposites add up to 0,remove them form the expression

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

Rewrite the expression

x \times x^{2} + x \times 5 x - x \times 5

Solution

x (x^{2} + 5 x - 5)

Show Solution

Find the roots

x_{1} = - \frac{5 + 3 5}{2}, x_{2} = 0, x_{3} = \frac{- 5 + 3 5}{2}

Alternative Form

x_{1} \approx - 5.854102, x_{2} = 0, x_{3} \approx 0.854102

Evaluate

(x^{2} - 5) (x + 5) + 25

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

(x^{2} - 5) (x + 5) + 25 = 0

Calculate

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Evaluate

(x^{2} - 5) (x + 5) + 25

Expand the expression

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Calculate

(x^{2} - 5) (x + 5)

Apply the distributive property

x^{2} \times x + x^{2} \times 5 - 5 x - 5 \times 5

Multiply the terms

x^{3} + x^{2} \times 5 - 5 x - 5 \times 5

Use the commutative property to reorder the terms

x^{3} + 5 x^{2} - 5 x - 5 \times 5

Multiply the numbers

x^{3} + 5 x^{2} - 5 x - 25

x^{3} + 5 x^{2} - 5 x - 25 + 25

Since two opposites add up to 0,remove them form the expression

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

x^{3} + 5 x^{2} - 5 x = 0

Factor the expression

x (x^{2} + 5 x - 5) = 0

Separate the equation into 2 possible cases

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

Solve the equation

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Evaluate

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

Substitute a= 1,b= 5 and c= - 5 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 5 \pm 5 ^{2} - 4 ( - 5 )}{2}

Simplify the expression

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Evaluate

5^{2} - 4 (- 5)

Multiply the numbers

5^{2} - (- 20)

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

5^{2} + 20

Evaluate the power

25 + 20

Add the numbers

45

x = \frac{- 5 \pm 45}{2}

Simplify the radical expression

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Evaluate

45

Write the expression as a product where the root of one of the factors can be evaluated

9 \times 5

Write the number in exponential form with the base of 3

3^{2} \times 5

The root of a product is equal to the product of the roots of each factor

3^{2} \times 5

Reduce the index of the radical and exponent with 2

35

x = \frac{- 5 \pm 3 5}{2}

Separate the equation into 2 possible cases

x = \frac{- 5 + 3 5}{2} x = \frac{- 5 - 3 5}{2}

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

x = \frac{- 5 + 3 5}{2} x = - \frac{5 + 3 5}{2}

x = 0 x = \frac{- 5 + 3 5}{2} x = - \frac{5 + 3 5}{2}

Solution

x_{1} = - \frac{5 + 3 5}{2}, x_{2} = 0, x_{3} = \frac{- 5 + 3 5}{2}

Alternative Form

x_{1} \approx - 5.854102, x_{2} = 0, x_{3} \approx 0.854102

Show Solution