Solve \sqrt{44-2x}=x-10

Question

Solve the equation

x = 14

Evaluate

44 - 2 x = x - 10

Find the domain

More Steps

Evaluate

44 - 2 x \geq 0

Move the constant to the right side

- 2 x \geq 0 - 44

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

- 2 x \geq - 44

Change the signs on both sides of the inequality and flip the inequality sign

2 x \leq 44

Divide both sides

\frac{2 x}{2} \leq \frac{44}{2}

Divide the numbers

x \leq \frac{44}{2}

Divide the numbers

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Evaluate

\frac{44}{2}

Reduce the numbers

\frac{22}{1}

Calculate

22

x \leq 22

44 - 2 x = x - 10, x \leq 22

Evaluate

44 - 2 x = x - 10, x - 10 \geq 0

Evaluate

More Steps

Evaluate

x - 10 \geq 0

Move the constant to the right side

x \geq 0 + 10

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

x \geq 10

44 - 2 x = x - 10, x \geq 10

Solve the equation for x

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Evaluate

44 - 2 x = x - 10

Raise both sides of the equation to the 2 -th power to eliminate the isolated 2 -th root

(44 - 2 x)^{2} = (x - 10)^{2}

Evaluate the power

44 - 2 x = x^{2} - 20 x + 100

Move the expression to the left side

44 - 2 x - (x^{2} - 20 x + 100) = 0

Subtract the terms

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Evaluate

44 - 2 x - (x^{2} - 20 x + 100)

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

44 - 2 x - x^{2} + 20 x - 100

Subtract the numbers

- 56 - 2 x - x^{2} + 20 x

Add the terms

- 56 + 18 x - x^{2}

- 56 + 18 x - x^{2} = 0

Factor the expression

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Evaluate

- 56 + 18 x - x^{2}

Rewrite the expression

- 56 + (14 + 4) x - x^{2}

Calculate

- 56 + 14 x + 4 x - x^{2}

Rewrite the expression

- 14 \times 4 + 14 x + x \times 4 - x \times x

Factor out - 14 from the expression

- 14 (4 - x) + x \times 4 - x \times x

Factor out x from the expression

- 14 (4 - x) + x (4 - x)

Factor out 4 - x from the expression

(- 14 + x) (4 - x)

(- 14 + x) (4 - x) = 0

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

- 14 + x = 0 4 - x = 0

Solve the equation for x

More Steps

Evaluate

- 14 + x = 0

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

x = 0 + 14

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

x = 14

x = 14 4 - x = 0

Solve the equation for x

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Evaluate

4 - x = 0

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

- x = 0 - 4

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

- x = - 4

Change the signs on both sides of the equation

x = 4

x = 14 x = 4

x = 14 x = 4, x \geq 10

Find the intersection

x = 14

Check if the solution is in the defined range

x = 14, x \leq 22

Find the intersection of the solution and the defined range

x = 14

Solution

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Check the solution

44 - 2 \times 14 = 14 - 10

Simplify

4 = 4

Evaluate

true

x = 14

Show Solution

Solve the equation

Graph