Solve -4(x-25)^2 - 600

Question

Simplify the expression

- 4 x^{2} + 200 x - 3100

Evaluate

- 4 (x - 25)^{2} - 600

Expand the expression

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Calculate

- 4 (x - 25)^{2}

Simplify

- 4 (x^{2} - 50 x + 625)

Apply the distributive property

- 4 x^{2} - (- 4 \times 50 x) - 4 \times 625

Multiply the numbers

- 4 x^{2} - (- 200 x) - 4 \times 625

Multiply the numbers

- 4 x^{2} - (- 200 x) - 2500

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

- 4 x^{2} + 200 x - 2500

- 4 x^{2} + 200 x - 2500 - 600

Solution

- 4 x^{2} + 200 x - 3100

Show Solution

Factor the expression

- 4 (x^{2} - 50 x + 775)

Evaluate

- 4 (x - 25)^{2} - 600

Simplify

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Evaluate

- 4 (x - 25)^{2}

Simplify

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Evaluate

(x - 25)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

x^{2} - 2 x \times 25 + 2 5^{2}

Calculate

x^{2} - 50 x + 625

- 4 (x^{2} - 50 x + 625)

Apply the distributive property

- 4 x^{2} - 4 (- 50 x) - 4 \times 625

Multiply the terms

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Evaluate

- 4 (- 50)

Multiplying or dividing an even number of negative terms equals a positive

4 \times 50

Multiply the numbers

200

- 4 x^{2} + 200 x - 4 \times 625

Multiply the terms

- 4 x^{2} + 200 x - 2500

- 4 x^{2} + 200 x - 2500 - 600

Subtract the numbers

- 4 x^{2} + 200 x - 3100

Solution

- 4 (x^{2} - 50 x + 775)

Show Solution

Find the roots

x_{1} = 25 - 56 \times i, x_{2} = 25 + 56 \times i

Alternative Form

x_{1} \approx 25 - 12.247449 i, x_{2} \approx 25 + 12.247449 i

Evaluate

- 4 (x - 25)^{2} - 600

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

- 4 (x - 25)^{2} - 600 = 0

Add or subtract both sides

- 4 (x - 25)^{2} = 0 + 600

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

- 4 (x - 25)^{2} = 600

Change the sign

4 (x - 25)^{2} = - 600

Divide both sides

\frac{4 ( x - 25 ) ^{2}}{4} = \frac{- 600}{4}

Divide the numbers

(x - 25)^{2} = \frac{- 600}{4}

Divide the numbers

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Evaluate

\frac{- 600}{4}

Reduce the numbers

\frac{- 150}{1}

Calculate

- 150

(x - 25)^{2} = - 150

Take the root of both sides of the equation and remember to use both positive and negative roots

x - 25 = \pm - 150

Simplify the expression

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Evaluate

- 150

Evaluate the power

150 \times - 1

Evaluate the power

150 \times i

Evaluate the power

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Evaluate

150

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

25 \times 6

Write the number in exponential form with the base of 5

5^{2} \times 6

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

5^{2} \times 6

Reduce the index of the radical and exponent with 2

56

56 \times i

x - 25 = \pm (56 \times i)

Separate the equation into 2 possible cases

x - 25 = 56 \times i x - 25 = - 56 \times i

Calculate

More Steps

Evaluate

x - 25 = 56 \times i

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

x = 56 \times i + 25

Calculate

x = 25 + 56 \times i

x = 25 + 56 \times i x - 25 = - 56 \times i

Calculate

More Steps

Evaluate

x - 25 = - 56 \times i

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

x = - 56 \times i + 25

Calculate

x = 25 - 56 \times i

x = 25 + 56 \times i x = 25 - 56 \times i

Solution

x_{1} = 25 - 56 \times i, x_{2} = 25 + 56 \times i

Alternative Form

x_{1} \approx 25 - 12.247449 i, x_{2} \approx 25 + 12.247449 i

Show Solution