Finite Math Examples

$x^{2} = 0.16$

Step 1

Subtract $0.16$ from both sides of the equation.

$x^{2} - 0.16 = 0$

Step 2

Rewrite $0.16$ as ${0.4}^{2}$ .

$x^{2} - {0.4}^{2} = 0$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 0.4$ .

$(x + 0.4) (x - 0.4) = 0$

Step 4

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

$x + 0.4 = 0$

$x - 0.4 = 0$

Step 5

Set $x + 0.4$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x + 0.4$ equal to $0$ .

$x + 0.4 = 0$

Step 5.2

Subtract $0.4$ from both sides of the equation.

$x = - 0.4$

Step 6

Set $x - 0.4$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 0.4$ equal to $0$ .

$x - 0.4 = 0$

Step 6.2

Add $0.4$ to both sides of the equation.

$x = 0.4$

Step 7

The final solution is all the values that make $(x + 0.4) (x - 0.4) = 0$ true.

$x = - 0.4, 0.4$