1)r²-100=0 solve by extracting square roots
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1)r²-100=0 solve by extracting square roots
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Steps by Extracting Square Roots:
Add to both sides. Anything plus gives itself.
Take the square root of both sides of the equation.
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Answer:
What is r²-100=0?
r² - 100 = 0 is a quadratic equation in the variable r that is in standard form, ax² + bx + c = 0, where a, b, and c are real numbers and a ≠0, and since this equation is a second-degree equation in one variable, r, then it will have two solutions, i.e., r will have two values that will make the given equation a true statement. These two values for the variable r are found as follows:
r² - 100 + 100 = 0 + 100
r² + 0 = 100
r² = 100
√r² = ±√100
r = ±10 that is:
r = -10 or r = 10
CHECK:
For r = -10:
r² - 100 = 0
(-10)² - 100 = 0
(-10)(-10) - 100 = 0
100 - 100 = 0
0 = 0
For r = 10:
r² - 100 = 0
(10)² - 100 = 0
(10)(10) - 100 = 0
100 - 100 = 0
0 = 0
Therefore, the solution set for the original, given equation is: {-10, 10}.