Question
Question Use the square roots property to solve the quadratic equation \( (2 a+2)^{2}=100 \). If there are multiple answers, list them separated by a comma, e.g. 1, 2. If there is no solution, enter \( \varnothing \).
Ask by Marsh Coles. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are: 4, -6.
Solution
Take the square root of both sides of the equation (2a + 2)² = 100.
Step 1: Apply the square root property:
2a + 2 = √100 or 2a + 2 = -√100
Step 2: Simplify the square root:
√100 = 10,
so the two equations are:
2a + 2 = 10
2a + 2 = -10
Step 3: Solve for a in each case:
For 2a + 2 = 10:
Subtract 2 from both sides: 2a = 8, then divide by 2: a = 4.
For 2a + 2 = -10:
Subtract 2 from both sides: 2a = -12, then divide by 2: a = -6.
The solutions are: 4, -6.
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Simplify this solution Extra Insights
To solve the quadratic equation \( (2a + 2)^2 = 100 \), we first take the square root of both sides. This gives us two equations to work with: 1. \( 2a + 2 = 10 \) 2. \( 2a + 2 = -10 \) Now, we solve each equation separately: For the first equation: \( 2a + 2 = 10 \) Subtract 2 from both sides: \( 2a = 8 \) Now divide by 2: \( a = 4 \) For the second equation: \( 2a + 2 = -10 \) Subtract 2 from both sides: \( 2a = -12 \) Now divide by 2: \( a = -6 \) Thus, the solutions to the equation are \( 4, -6 \).
