Algebra Examples

$7 x^{2} - 2 x + 21 = 26 x + 1$

Step 1

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

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Step 1.1

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

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Step 1.1.1

Subtract $26 x$ from both sides of the equation.

$7 x^{2} - 2 x + 21 - 26 x = 1$

Step 1.1.2

Subtract $1$ from both sides of the equation.

$7 x^{2} - 2 x + 21 - 26 x - 1 = 0$

Step 1.2

Simplify $7 x^{2} - 2 x + 21 - 26 x - 1$ .

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Step 1.2.1

Subtract $26 x$ from $- 2 x$ .

$7 x^{2} - 28 x + 21 - 1 = 0$

Step 1.2.2

Subtract $1$ from $21$ .

$7 x^{2} - 28 x + 20 = 0$

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 $a = 7$ , $b = - 28$ , and $c = 20$ into the quadratic formula and solve for $x$ .

$\frac{28 \pm \sqrt{{(- 28)}^{2} - 4 \cdot (7 \cdot 20)}}{2 \cdot 7}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 28$ to the power of $2$ .

$x = \frac{28 \pm \sqrt{784 - 4 \cdot 7 \cdot 20}}{2 \cdot 7}$

Step 4.1.2

Multiply $- 4 \cdot 7 \cdot 20$ .

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Step 4.1.2.1

Multiply $- 4$ by $7$ .

$x = \frac{28 \pm \sqrt{784 - 28 \cdot 20}}{2 \cdot 7}$

Step 4.1.2.2

Multiply $- 28$ by $20$ .

$x = \frac{28 \pm \sqrt{784 - 560}}{2 \cdot 7}$

Step 4.1.3

Subtract $560$ from $784$ .

$x = \frac{28 \pm \sqrt{224}}{2 \cdot 7}$

Step 4.1.4

Rewrite $224$ as $4^{2} \cdot 14$ .

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Step 4.1.4.1

Factor $16$ out of $224$ .

$x = \frac{28 \pm \sqrt{16 (14)}}{2 \cdot 7}$

Step 4.1.4.2

Rewrite $16$ as $4^{2}$ .

$x = \frac{28 \pm \sqrt{4^{2} \cdot 14}}{2 \cdot 7}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{28 \pm 4 \sqrt{14}}{2 \cdot 7}$

Step 4.2

Multiply $2$ by $7$ .

$x = \frac{28 \pm 4 \sqrt{14}}{14}$

Step 4.3

Simplify $\frac{28 \pm 4 \sqrt{14}}{14}$ .

$x = \frac{14 \pm 2 \sqrt{14}}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{14 \pm 2 \sqrt{14}}{7}$

Decimal Form:

$x = 3.06904496 \dots, 0.93095503 \dots$