Algebra Examples

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

Step 1

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

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Step 1.1

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

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Step 1.1.1

Simplify the left side.

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Step 1.1.1.1

Simplify $x (2 x - 7)$ .

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Step 1.1.1.1.1

Simplify by multiplying through.

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Step 1.1.1.1.1.1

Apply the distributive property.

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

Step 1.1.1.1.1.2

Reorder.

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Step 1.1.1.1.1.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.1.1.1.1.2.2

Move $- 7$ to the left of $x$ .

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

Step 1.1.1.1.2

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

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Step 1.1.1.1.2.1

Move $x$ .

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

Step 1.1.1.1.2.2

Multiply $x$ by $x$ .

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

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

Step 1.1.2

Add $3$ to both sides of the equation.

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

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.

$a = 2$ , $b = - 7$ , $c = 3$

Step 2

List the results.

Sum of the roots is $\frac{7}{2}$

Product of the roots is $\frac{3}{2}$