Answered

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Solve the equation using square roots.

[tex]\[ x^2 - 15 = 34 \][/tex]

A. 7
B. [tex]\(\pm 7\)[/tex]
C. [tex]\(\pm 49\)[/tex]
D. No real number solutions

Sagot :

GinnyAnswer
Certainly! Let's solve the equation [tex]\( x^2 - 15 = 34 \)[/tex] step-by-step.

1. Start with the given equation:
[tex]\[ x^2 - 15 = 34 \][/tex]

2. Isolate the [tex]\( x^2 \)[/tex] term by adding 15 to both sides of the equation:
[tex]\[ x^2 = 34 + 15 \][/tex]

3. Simplify the right side of the equation:
[tex]\[ x^2 = 49 \][/tex]

4. To solve for [tex]\( x \)[/tex], we take the square root of both sides. Remember that taking the square root yields two solutions, one positive and one negative:
[tex]\[ x = \pm \sqrt{49} \][/tex]

5. Simplify the square root:
[tex]\[ x = \pm 7 \][/tex]

So, the solutions to the equation [tex]\( x^2 - 15 = 34 \)[/tex] are:
[tex]\[ x = -7 \quad \text{and} \quad x = 7 \][/tex]
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