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Solve each equation by extracting the square roots.
1. x² = -31
2. (x - 6)² - 7 = 0
3. 5x² - 1 = 4
4. 36 =x² -4
5. (2x + 1)² = 121
*Show your solution and how you solve it*​

Sagot :

Aziyamunez03idn

【Explanation】:

1. The equation \(x^2 = -31\) has no real solutions since the square of a real number cannot be negative. However, it does have complex solutions, which are ± (i sqrt(31)).

2. For the equation \((x-6)^2-7=0\), by rearranging and taking the square root, we get two solutions: \(x = 6 - \sqrt{7}\) and \(x = 6 + \sqrt{7}\).

3. The equation \(5x^2-1=4\) can be rearranged to \(5x^2 = 5\), which gives \(x^2 = 1\). Taking the square root, we get two solutions: \(x = 1\) and \(x = -1\).

4. For the equation \(36=x^2-4\), rearranging gives \(x^2 = 40\). Taking the square root, we get two solutions: \(x = 2 \sqrt{10}\) and \(x = -2 \sqrt{10}\).

5. The equation \((2x+1)^2=121\) can be simplified to \((2x+1)^2 = 11^2\). Taking the square root, we get two solutions: \(x = 5\) and \(x = -6\).

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