Question
Find one value of \( x \) that is a solution to the equation: \( \begin{array}{l}(2 x+3)^{2}-6 x-9=0 \\ x=\end{array} \)
Ask by Brewer Summers. in the United States
Feb 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
One solution is \( x = -\frac{3}{2} \).
Solution
Solve the equation \( (2x+3)^2-6x-9=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(\left(2x+3\right)^{2}-6x-9=0\)
- step1: Expand the expression:
\(4x^{2}+6x=0\)
- step2: Factor the expression:
\(2x\left(2x+3\right)=0\)
- step3: Separate into possible cases:
\(\begin{align}&2x=0\\&2x+3=0\end{align}\)
- step4: Solve the equation:
\(\begin{align}&x=0\\&x=-\frac{3}{2}\end{align}\)
- step5: Rewrite:
\(x_{1}=-\frac{3}{2},x_{2}=0\)
The solutions to the equation \( (2x+3)^2-6x-9=0 \) are \( x = -\frac{3}{2} \) and \( x = 0 \).
Therefore, one value of \( x \) that is a solution to the equation is \( x = -\frac{3}{2} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To solve the equation \((2x+3)^{2}-6x-9=0\), we first expand and simplify the left side. 1. Expand the squared term: \((2x+3)^{2} = 4x^{2} + 12x + 9\). 2. Substitute it back into the equation: \(4x^{2} + 12x + 9 - 6x - 9 = 0\). 3. Simplify the equation: \(4x^{2} + (12x - 6x) + (9 - 9) = 0\), \(4x^{2} + 6x = 0\). 4. Factor out the common term: \(2x(2x + 3) = 0\). 5. Set each factor to zero: \(2x = 0 \implies x = 0\), \(2x + 3 = 0 \implies 2x = -3 \implies x = -\frac{3}{2}\). Thus, one value of \( x \) that is a solution to the equation is \( x = 0 \).
