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Original Question
Solve the following quadratic equation using square roots: (x +3)^2 =36.
Q1 Solve the following quadratic equation using square roots: (x-5)2= 49
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Answered by
GPT-4o mini
To solve the quadratic equation \((x - 5)^2 = 49\) using square roots, follow these steps:
1. Take the square root of both sides of the equation. Remember to consider both the positive and negative roots:
\[
x - 5 = \pm 7
\]
2. Now you will have two separate equations to solve:
a) \(x - 5 = 7\)
b) \(x - 5 = -7\)
3. Solve each equation:
a) For \(x - 5 = 7\):
\[
x = 7 + 5 = 12
\]
b) For \(x - 5 = -7\):
\[
x = -7 + 5 = -2
\]
4. The solutions to the equation \((x - 5)^2 = 49\) are:
\[
x = 12 \quad \text{and} \quad x = -2
\]
1. Take the square root of both sides of the equation. Remember to consider both the positive and negative roots:
\[
x - 5 = \pm 7
\]
2. Now you will have two separate equations to solve:
a) \(x - 5 = 7\)
b) \(x - 5 = -7\)
3. Solve each equation:
a) For \(x - 5 = 7\):
\[
x = 7 + 5 = 12
\]
b) For \(x - 5 = -7\):
\[
x = -7 + 5 = -2
\]
4. The solutions to the equation \((x - 5)^2 = 49\) are:
\[
x = 12 \quad \text{and} \quad x = -2
\]
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