Algebra Examples

$- 34 = x^{2} - 14 x + 10$

Step 1

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

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Step 1.1

Subtract $x^{2}$ from both sides of the equation.

$- 34 - x^{2} = - 14 x + 10$

Step 1.2

Add $14 x$ to both sides of the equation.

$- 34 - x^{2} + 14 x = 10$

Step 1.3

Subtract $10$ from both sides of the equation.

$- 34 - x^{2} + 14 x - 10 = 0$

Step 2

Subtract $10$ from $- 34$ .

$- x^{2} + 14 x - 44 = 0$

Step 3

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = - 1$

$b = 14$

$c = - 44 = 0$

Step 4

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e = 0$

Step 5

Find the value of $d$ using the formula $d = \frac{b}{2 a}$ .

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Step 5.1

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{14}{2 \cdot - 1}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Cancel the common factor of $14$ and $2$ .

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Step 5.2.1.1

Factor $2$ out of $14$ .

$d = \frac{2 \cdot 7}{2 \cdot - 1}$

Step 5.2.1.2

Move the negative one from the denominator of $\frac{7}{- 1}$ .

$d = - 1 \cdot 7$

Step 5.2.2

Multiply $- 1$ by $7$ .

$d = - 7$

Step 6

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

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Step 6.1

Substitute the values of $c$ , $b$ and $a$ into the formula $e = c - \frac{b^{2}}{4 a}$ .

$e = - 44 - \frac{14^{2}}{4 \cdot - 1}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify each term.

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Step 6.2.1.1

Raise $14$ to the power of $2$ .

$e = - 44 - \frac{196}{4 \cdot - 1}$

Step 6.2.1.2

Multiply $4$ by $- 1$ .

$e = - 44 - \frac{196}{- 4}$

Step 6.2.1.3

Divide $196$ by $- 4$ .

$e = - 44 - - 49$

Step 6.2.1.4

Multiply $- 1$ by $- 49$ .

$e = - 44 + 49$

Step 6.2.2

Add $- 44$ and $49$ .

$e = 5$

Step 7

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $- {(x - 7)}^{2} + 5$ .

$- {(x - 7)}^{2} + 5 = 0$