Solved on Jan 23, 2024

Solve the quadratic equation x2+3=19x^{2} + 3 = 19 and select the correct solution(s).

STEP 1

Assumptions
1. We are given the equation x2+3=19x^{2} + 3 = 19.
2. We need to solve for xx.
3. The solution will be in the form of the options provided: A, B, C, D, or E.

STEP 2

To solve for xx, we need to isolate x2x^2 on one side of the equation. We can do this by subtracting 3 from both sides of the equation.
x2+33=193x^{2} + 3 - 3 = 19 - 3

STEP 3

Perform the subtraction to simplify the equation.
x2=16x^{2} = 16

STEP 4

Now we need to take the square root of both sides of the equation to solve for xx. Remember that taking the square root of a number gives us two solutions: one positive and one negative.
x=±16x = \pm\sqrt{16}

STEP 5

Calculate the square root of 16.
x=±16=±4x = \pm\sqrt{16} = \pm4
The solution to the equation x2+3=19x^{2} + 3 = 19 is x=±4x = \pm4.
The correct answer is A. ±4\pm 4.

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