Solve \sqrt 20 - x + \sqrt 4 - x = 8

Question

Solve the equation

x = - 3 + 5

Alternative Form

x \approx - 0.763932

Evaluate

20 - x + 4 - x = 8

Simplify

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Evaluate

20 - x + 4 - x

Simplify the root

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Evaluate

20

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

4 \times 5

Write the number in exponential form with the base of 2

2^{2} \times 5

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

2^{2} \times 5

Reduce the index of the radical and exponent with 2

25

25 - x + 4 - x

Evaluate the square root

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Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

25 - x + 2 - x

Subtract the terms

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Evaluate

- x - x

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

(- 1 - 1) x

Subtract the numbers

- 2 x

25 - 2 x + 2

25 - 2 x + 2 = 8

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

- 2 x = 8 - (25 + 2)

Subtract the terms

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Evaluate

8 - (25 + 2)

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

8 - 25 - 2

Subtract the numbers

6 - 25

- 2 x = 6 - 25

Change the signs on both sides of the equation

2 x = - 6 + 25

Divide both sides

\frac{2 x}{2} = \frac{- 6 + 2 5}{2}

Divide the numbers

x = \frac{- 6 + 2 5}{2}

Solution

More Steps

Evaluate

\frac{- 6 + 2 5}{2}

Rewrite the expression

\frac{2 ( - 3 + 5 )}{2}

Reduce the fraction

- 3 + 5

x = - 3 + 5

Alternative Form

x \approx - 0.763932

Show Solution

Solve the equation

Graph