Algebra Examples

$- x + 4 x (2 - x) = - 1$

Step 1

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

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $- x + 4 x (2 - x)$ .

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Step 1.1.1.1

Simplify each term.

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Step 1.1.1.1.1

Apply the distributive property.

$- x + 4 x \cdot 2 + 4 x (- x) = - 1$

Step 1.1.1.1.2

Multiply $2$ by $4$ .

$- x + 8 x + 4 x (- x) = - 1$

Step 1.1.1.1.3

Rewrite using the commutative property of multiplication.

$- x + 8 x + 4 \cdot - 1 x \cdot x = - 1$

Step 1.1.1.1.4

Simplify each term.

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Step 1.1.1.1.4.1

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

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Step 1.1.1.1.4.1.1

Move $x$ .

$- x + 8 x + 4 \cdot - 1 (x \cdot x) = - 1$

Step 1.1.1.1.4.1.2

Multiply $x$ by $x$ .

$- x + 8 x + 4 \cdot - 1 x^{2} = - 1$

Step 1.1.1.1.4.2

Multiply $4$ by $- 1$ .

$- x + 8 x - 4 x^{2} = - 1$

Step 1.1.1.2

Add $- x$ and $8 x$ .

$7 x - 4 x^{2} = - 1$

Step 1.2

Add $1$ to both sides of the equation.

$7 x - 4 x^{2} + 1 = 0$

Step 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 3

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

$a = - 4$ , $b = 7$ , $c = 1$