Algebra Examples

7 x^{2} - 3 x + 8 = 9 x^{2} + 15

$7 x^{2} - 3 x + 8 = 9 x^{2} + 15$

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

9 x^{2}

$9 x^{2}$ from both sides of the equation.

7 x^{2} - 3 x + 8 - 9 x^{2} = 15

$7 x^{2} - 3 x + 8 - 9 x^{2} = 15$

Step 1.1.2

Subtract

15

$15$ from both sides of the equation.

7 x^{2} - 3 x + 8 - 9 x^{2} - 15 = 0

$7 x^{2} - 3 x + 8 - 9 x^{2} - 15 = 0$

7 x^{2} - 3 x + 8 - 9 x^{2} - 15 = 0

$7 x^{2} - 3 x + 8 - 9 x^{2} - 15 = 0$

Step 1.2

Simplify

7 x^{2} - 3 x + 8 - 9 x^{2} - 15

$7 x^{2} - 3 x + 8 - 9 x^{2} - 15$ .

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Step 1.2.1

Subtract

9 x^{2}

$9 x^{2}$ from

7 x^{2}

$7 x^{2}$ .

- 2 x^{2} - 3 x + 8 - 15 = 0

$- 2 x^{2} - 3 x + 8 - 15 = 0$

Step 1.2.2

Subtract

15

$15$ from

8

$8$ .

- 2 x^{2} - 3 x - 7 = 0

$- 2 x^{2} - 3 x - 7 = 0$

- 2 x^{2} - 3 x - 7 = 0

$- 2 x^{2} - 3 x - 7 = 0$

- 2 x^{2} - 3 x - 7 = 0

$- 2 x^{2} - 3 x - 7 = 0$

Step 2

Once the quadratic is in standard form, the values of

a

$a$ ,

b

$b$ , and

c

$c$ can be found.

a x^{2} + b x + c

$a x^{2} + b x + c$

Step 3

Use the standard form of the equation to find

a

$a$ ,

b

$b$ , and

c

$c$ for this quadratic.

a = - 2

$a = - 2$ ,

b = - 3

$b = - 3$ ,

c = - 7

$c = - 7$