Algebra Examples

$10 x^{2} - 2 x + 2 = 3 x - 4$

Step 1

Find $a$ , $b$ , and $c$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

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

Tap for more steps...

Step 1.1.1.1

Subtract $3 x$ from both sides of the equation.

$10 x^{2} - 2 x + 2 - 3 x = - 4$

Step 1.1.1.2

Add $4$ to both sides of the equation.

$10 x^{2} - 2 x + 2 - 3 x + 4 = 0$

Step 1.1.2

Simplify $10 x^{2} - 2 x + 2 - 3 x + 4$ .

Tap for more steps...

Step 1.1.2.1

Subtract $3 x$ from $- 2 x$ .

$10 x^{2} - 5 x + 2 + 4 = 0$

Step 1.1.2.2

Add $2$ and $4$ .

$10 x^{2} - 5 x + 6 = 0$

Step 1.2

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

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

Step 1.3

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 10$ , $b = - 5$ , $c = 6$

Step 2

Substitute the values into the sum of roots formula $- \frac{b}{a}$ .

Tap for more steps...

Step 2.1

Cancel the common factor of $5$ and $10$ .

Tap for more steps...

Step 2.1.1

Factor $5$ out of $5$ .

$\frac{5 (1)}{10}$

Step 2.1.2

Cancel the common factors.

Tap for more steps...

Step 2.1.2.1

Factor $5$ out of $10$ .

$\frac{5 \cdot 1}{5 \cdot 2}$

Step 2.1.2.2

Cancel the common factor.

$\frac{5 \cdot 1}{5 \cdot 2}$

Step 2.1.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 3

Substitute the values into the product of roots formula $\frac{c}{a}$ .

Tap for more steps...

Step 3.1

Cancel the common factor of $6$ and $10$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $6$ .

$\frac{2 (3)}{10}$

Step 3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.1

Factor $2$ out of $10$ .

$\frac{2 \cdot 3}{2 \cdot 5}$

Step 3.1.2.2

Cancel the common factor.

$\frac{2 \cdot 3}{2 \cdot 5}$

Step 3.1.2.3

Rewrite the expression.

$\frac{3}{5}$

Step 4

List the results.

Sum of the roots is $\frac{1}{2}$

Product of the roots is $\frac{3}{5}$