Pre-Algebra Examples

$(x - (4 - \sqrt{21})) (x - (4 + \sqrt{21})) = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - (4 - \sqrt{21}) = 0$

$x - (4 + \sqrt{21}) = 0$

Step 2

Set $x - (4 - \sqrt{21})$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $x - (4 - \sqrt{21})$ equal to $0$ .

$x - (4 - \sqrt{21}) = 0$

Step 2.2

Solve $x - (4 - \sqrt{21}) = 0$ for $x$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Apply the distributive property.

$x - 1 \cdot 4 - - \sqrt{21} = 0$

Step 2.2.1.2

Multiply $- 1$ by $4$ .

$x - 4 - - \sqrt{21} = 0$

Step 2.2.1.3

Multiply $- - \sqrt{21}$ .

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Step 2.2.1.3.1

Multiply $- 1$ by $- 1$ .

$x - 4 + 1 \sqrt{21} = 0$

Step 2.2.1.3.2

Multiply $\sqrt{21}$ by $1$ .

$x - 4 + \sqrt{21} = 0$

Step 2.2.2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.2.2.1

Add $4$ to both sides of the equation.

$x + \sqrt{21} = 4$

Step 2.2.2.2

Subtract $\sqrt{21}$ from both sides of the equation.

$x = 4 - \sqrt{21}$

Step 3

Set $x - (4 + \sqrt{21})$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $x - (4 + \sqrt{21})$ equal to $0$ .

$x - (4 + \sqrt{21}) = 0$

Step 3.2

Solve $x - (4 + \sqrt{21}) = 0$ for $x$ .

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Apply the distributive property.

$x - 1 \cdot 4 - \sqrt{21} = 0$

Step 3.2.1.2

Multiply $- 1$ by $4$ .

$x - 4 - \sqrt{21} = 0$

Step 3.2.2

Move all terms not containing $x$ to the right side of the equation.

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Step 3.2.2.1

Add $4$ to both sides of the equation.

$x - \sqrt{21} = 4$

Step 3.2.2.2

Add $\sqrt{21}$ to both sides of the equation.

$x = 4 + \sqrt{21}$

Step 4

The final solution is all the values that make $(x - (4 - \sqrt{21})) (x - (4 + \sqrt{21})) = 0$ true.

$x = 4 - \sqrt{21}, 4 + \sqrt{21}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 4 - \sqrt{21}, 4 + \sqrt{21}$

Decimal Form:

$x = - 0.58257569 \dots, 8.58257569 \dots$