First we need to factor trinomial $ \color{blue}{ x^2+10x-375 } $ and than we use factored form to solve an equation $ \color{blue}{ x^2+10x-375 = 0} $.
Step 1: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:
$$ \color{blue}{ b = 10 } ~ \text{ and } ~ \color{red}{ c = -375 }$$Now we must discover two numbers that sum up to $ \color{blue}{ 10 } $ and multiply to $ \color{red}{ -375 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -375 }$.
PRODUCT = -375 | |
-1 375 | 1 -375 |
-3 125 | 3 -125 |
-5 75 | 5 -75 |
-15 25 | 15 -25 |
Step 3: Find out which pair sums up to $\color{blue}{ b = 10 }$
PRODUCT = -375 and SUM = 10 | |
-1 375 | 1 -375 |
-3 125 | 3 -125 |
-5 75 | 5 -75 |
-15 25 | 15 -25 |
Step 4: Put -15 and 25 into placeholders to get factored form.
$$ \begin{aligned} x^{2}+10x-375 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+10x-375 & = (x -15)(x + 25) \end{aligned} $$Step 5: Set each factor to zero and solve equations.
$$ \begin{array}{ccc} \begin{aligned} x-15 &= 0 \\ x &= 15 \end{aligned} & ~ & \begin{aligned} x+25 &= 0 \\ x &= -25 \end{aligned} \end{array} $$