QQuestionMathematics
QuestionMathematics
# New Tab
## Knowledge Check
## Solve for $\boldsymbol{x}$
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:: Identify the given information and the equation to solve.
Our goal is to solve for $x$.
We are given the equation:
Step 2:: Expand the left side of the equation using the distributive property (also known as the FOIL method).
$$3x^2 + 10x - 8 = 2x^2 + 15x - 8$$
(3x - 2)(x + 4) &= 3x^2 + 12x - 2x - 8 \ &= 3x^2 + 10x - 8 \end{align*} So, the original equation becomes:
Step 3:: Move the $2x^1$ term to the left side and the $- 1$ term to the right side of the equation.
$$x^2 - 5x = 0$$
This simplifies to:
Step 4:: Factor out an $x$ from both terms on the left side of the equation.
$$x(x - 5) = 0$$
Step 5:: Recall that if a product of factors equals zero, then at least one of the factors must be equal to zero.
$$x = 0 \quad \text{or} \quad x - 5 = 0$$
Step 6:: Solve for $x$ in both cases.
$\begin{align*}
x - 5 &= 0 \ x &= 5 \end{align*}
Final Answer
The solutions to the equation are $x = 1$ and $ x = 1$.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students