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Simplifying (x + -2)(x + -2) = 33 Reorder the terms: (-2 + x)(x + -2) = 33 Reorder the terms: (-2 + x)(-2 + x) = 33 Multiply (-2 + x) * (-2 + x) (-2(-2 + x) + x(-2 + x)) = 33 ((-2 * -2 + x * -2) + x(-2 + x)) = 33 ((4 + -2x) + x(-2 + x)) = 33 (4 + -2x + (-2 * x + x * x)) = 33 (4 + -2x + (-2x + x2)) = 33 Combine like terms: -2x + -2x = -4x (4 + -4x + x2) = 33 Solving 4 + -4x + x2 = 33 Solving for variable 'x'. Reorder the terms: 4 + -33 + -4x + x2 = 33 + -33 Combine like terms: 4 + -33 = -29 -29 + -4x + x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -29 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -4x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -4x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -4x + x2 = 0 + 29 -4x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -4x + x2 = 29 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 29 + 4 Reorder the terms: 4 + -4x + x2 = 29 + 4 Combine like terms: 29 + 4 = 33 4 + -4x + x2 = 33 Factor a perfect square on the left side: (x + -2)(x + -2) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + -2) equal to 5.744562647 and -5.744562647.Subproblem 1
x + -2 = 5.744562647 Simplifying x + -2 = 5.744562647 Reorder the terms: -2 + x = 5.744562647 Solving -2 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.744562647 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.744562647 + 2 x = 5.744562647 + 2 Combine like terms: 5.744562647 + 2 = 7.744562647 x = 7.744562647 Simplifying x = 7.744562647Subproblem 2
x + -2 = -5.744562647 Simplifying x + -2 = -5.744562647 Reorder the terms: -2 + x = -5.744562647 Solving -2 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.744562647 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.744562647 + 2 x = -5.744562647 + 2 Combine like terms: -5.744562647 + 2 = -3.744562647 x = -3.744562647 Simplifying x = -3.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.744562647, -3.744562647}
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