Solve for b (8x^2-15x)-(x^2-27x)=ax^2+bx

$(8 x^{2} - 15 x) - (x^{2} - 27 x) = a x^{2} + b x$

Step 1

Rewrite the equation as $a x^{2} + b x = 8 x^{2} - 15 x - (x^{2} - 27 x)$ .

$a x^{2} + b x = 8 x^{2} - 15 x - (x^{2} - 27 x)$

Step 2

Simplify $8 x^{2} - 15 x - (x^{2} - 27 x)$ .

Simplify each term.

Apply the distributive property.

$a x^{2} + b x = 8 x^{2} - 15 x - x^{2} - (- 27 x)$

Multiply $- 27$ by $- 1$ .

$a x^{2} + b x = 8 x^{2} - 15 x - x^{2} + 27 x$

Simplify by adding terms.

Subtract $x^{2}$ from $8 x^{2}$ .

$a x^{2} + b x = 7 x^{2} - 15 x + 27 x$

Add $- 15 x$ and $27 x$ .

$a x^{2} + b x = 7 x^{2} + 12 x$

Step 3

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

$b x = 7 x^{2} + 12 x - a x^{2}$

Step 4

Divide each term in $b x = 7 x^{2} + 12 x - a x^{2}$ by $x$ and simplify.

Divide each term in $b x = 7 x^{2} + 12 x - a x^{2}$ by $x$ .

$\frac{b x}{x} = \frac{7 x^{2}}{x} + \frac{12 x}{x} + \frac{- a x^{2}}{x}$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{b x}{x} = \frac{7 x^{2}}{x} + \frac{12 x}{x} + \frac{- a x^{2}}{x}$

Divide $b$ by $1$ .

$b = \frac{7 x^{2}}{x} + \frac{12 x}{x} + \frac{- a x^{2}}{x}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $7 x^{2}$ .

$b = \frac{x (7 x)}{x} + \frac{12 x}{x} + \frac{- a x^{2}}{x}$

Cancel the common factors.

Raise $x$ to the power of $1$ .

$b = \frac{x (7 x)}{x^{1}} + \frac{12 x}{x} + \frac{- a x^{2}}{x}$

Factor $x$ out of $x^{1}$ .

$b = \frac{x (7 x)}{x \cdot 1} + \frac{12 x}{x} + \frac{- a x^{2}}{x}$

Cancel the common factor.

$b = \frac{x (7 x)}{x \cdot 1} + \frac{12 x}{x} + \frac{- a x^{2}}{x}$

Rewrite the expression.

$b = \frac{7 x}{1} + \frac{12 x}{x} + \frac{- a x^{2}}{x}$

Divide $7 x$ by $1$ .

$b = 7 x + \frac{12 x}{x} + \frac{- a x^{2}}{x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$b = 7 x + \frac{12 x}{x} + \frac{- a x^{2}}{x}$

Divide $12$ by $1$ .

$b = 7 x + 12 + \frac{- a x^{2}}{x}$

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $- a x^{2}$ .

$b = 7 x + 12 + \frac{x (- a x)}{x}$

Cancel the common factors.

Raise $x$ to the power of $1$ .

$b = 7 x + 12 + \frac{x (- a x)}{x^{1}}$

Factor $x$ out of $x^{1}$ .

$b = 7 x + 12 + \frac{x (- a x)}{x \cdot 1}$

Cancel the common factor.

$b = 7 x + 12 + \frac{x (- a x)}{x \cdot 1}$

Rewrite the expression.

$b = 7 x + 12 + \frac{- a x}{1}$

Divide $- a x$ by $1$ .

$b = 7 x + 12 - a x$

Solve for b (8x^2-15x)-(x^2-27x)=ax^2+bx

Related Questions

Support LCMGCF.com by disabling your adblocker.