Question
Solve the quadratic equation by factoring. \[ t^{2}+7 t+4=t-5 \]
Ask by Reid Ross. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( t = -3 \)
Solution
Solve the equation \( t^{2}+7t+4=t-5 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(t^{2}+7t+4=t-5\)
- step1: Move the expression to the left side:
\(t^{2}+6t+9=0\)
- step2: Factor the expression:
\(\left(t+3\right)^{2}=0\)
- step3: Simplify the expression:
\(t+3=0\)
- step4: Move the constant to the right side:
\(t=0-3\)
- step5: Remove 0:
\(t=-3\)
The solution to the quadratic equation \(t^{2}+7t+4=t-5\) by factoring is \(t=-3\).
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Simplify this solution Mind Expander
First, let's rearrange the equation to set it to zero: \[ t^2 + 7t + 4 - t + 5 = 0 \] This simplifies to: \[ t^2 + 6t + 9 = 0 \] Next, we can factor the quadratic: \[ (t + 3)(t + 3) = 0 \] or \[ (t + 3)^2 = 0 \] Setting the factor equal to zero gives us: \[ t + 3 = 0 \] So, the solution is: \[ t = -3 \] The quadratic has one solution, a double root at \( t = -3 \).
