Pre-Algebra Examples

$- 4 x^{2} - 8 x - 3 = - 3 - 55 x^{2} \cdot 2$

Step 1

Multiply $2$ by $- 55$ .

$- 4 x^{2} - 8 x - 3 = - 3 - 110 x^{2}$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Add $110 x^{2}$ to both sides of the equation.

$- 4 x^{2} - 8 x - 3 + 110 x^{2} = - 3$

Step 2.2

Add $- 4 x^{2}$ and $110 x^{2}$ .

$106 x^{2} - 8 x - 3 = - 3$

Step 3

Add $3$ to both sides of the equation.

$106 x^{2} - 8 x - 3 + 3 = 0$

Step 4

Combine the opposite terms in $106 x^{2} - 8 x - 3 + 3$ .

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Step 4.1

Add $- 3$ and $3$ .

$106 x^{2} - 8 x + 0 = 0$

Step 4.2

Add $106 x^{2} - 8 x$ and $0$ .

$106 x^{2} - 8 x = 0$

Step 5

Factor $2 x$ out of $106 x^{2} - 8 x$ .

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Step 5.1

Factor $2 x$ out of $106 x^{2}$ .

$2 x (53 x) - 8 x = 0$

Step 5.2

Factor $2 x$ out of $- 8 x$ .

$2 x (53 x) + 2 x (- 4) = 0$

Step 5.3

Factor $2 x$ out of $2 x (53 x) + 2 x (- 4)$ .

$2 x (53 x - 4) = 0$

Step 6

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

$x = 0$

$53 x - 4 = 0$

Step 7

Set $x$ equal to $0$ .

$x = 0$

Step 8

Set $53 x - 4$ equal to $0$ and solve for $x$ .

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Step 8.1

Set $53 x - 4$ equal to $0$ .

$53 x - 4 = 0$

Step 8.2

Solve $53 x - 4 = 0$ for $x$ .

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Step 8.2.1

Add $4$ to both sides of the equation.

$53 x = 4$

Step 8.2.2

Divide each term in $53 x = 4$ by $53$ and simplify.

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Step 8.2.2.1

Divide each term in $53 x = 4$ by $53$ .

$\frac{53 x}{53} = \frac{4}{53}$

Step 8.2.2.2

Simplify the left side.

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Step 8.2.2.2.1

Cancel the common factor of $53$ .

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Step 8.2.2.2.1.1

Cancel the common factor.

$\frac{53 x}{53} = \frac{4}{53}$

Step 8.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{53}$

Step 9

The final solution is all the values that make $2 x (53 x - 4) = 0$ true.

$x = 0, \frac{4}{53}$