Algebra Examples

$3 x (x - 2) = - 7 x + 1$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $3 x (x - 2)$ .

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Step 1.1.1.1

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 2 = - 7 x + 1$

Step 1.1.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1.1.2.1

Move $x$ .

$3 (x \cdot x) + 3 x \cdot - 2 = - 7 x + 1$

Step 1.1.1.2.2

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot - 2 = - 7 x + 1$

Step 1.1.1.3

Multiply $- 2$ by $3$ .

$3 x^{2} - 6 x = - 7 x + 1$

Step 1.2

Move all the expressions to the left side of the equation.

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Step 1.2.1

Add $7 x$ to both sides of the equation.

$3 x^{2} - 6 x + 7 x = 1$

Step 1.2.2

Subtract $1$ from both sides of the equation.

$3 x^{2} - 6 x + 7 x - 1 = 0$

Step 1.3

Add $- 6 x$ and $7 x$ .

$3 x^{2} + x - 1 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 3$ , $b = 1$ , and $c = - 1$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (3 \cdot - 1)}}{2 \cdot 3}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 3 \cdot - 1}}{2 \cdot 3}$

Step 4.1.2

Multiply $- 4 \cdot 3 \cdot - 1$ .

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Step 4.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{- 1 \pm \sqrt{1 - 12 \cdot - 1}}{2 \cdot 3}$

Step 4.1.2.2

Multiply $- 12$ by $- 1$ .

$x = \frac{- 1 \pm \sqrt{1 + 12}}{2 \cdot 3}$

Step 4.1.3

Add $1$ and $12$ .

$x = \frac{- 1 \pm \sqrt{13}}{2 \cdot 3}$

Step 4.2

Multiply $2$ by $3$ .

$x = \frac{- 1 \pm \sqrt{13}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 1 \pm \sqrt{13}}{6}$

Decimal Form:

$x = 0.43425854 \dots, - 0.76759187 \dots$