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Simplifying 2(x + 2)(x + 2) = -22x + 5 Reorder the terms: 2(2 + x)(x + 2) = -22x + 5 Reorder the terms: 2(2 + x)(2 + x) = -22x + 5 Multiply (2 + x) * (2 + x) 2(2(2 + x) + x(2 + x)) = -22x + 5 2((2 * 2 + x * 2) + x(2 + x)) = -22x + 5 2((4 + 2x) + x(2 + x)) = -22x + 5 2(4 + 2x + (2 * x + x * x)) = -22x + 5 2(4 + 2x + (2x + x2)) = -22x + 5 Combine like terms: 2x + 2x = 4x 2(4 + 4x + x2) = -22x + 5 (4 * 2 + 4x * 2 + x2 * 2) = -22x + 5 (8 + 8x + 2x2) = -22x + 5 Reorder the terms: 8 + 8x + 2x2 = 5 + -22x Solving 8 + 8x + 2x2 = 5 + -22x Solving for variable 'x'. Reorder the terms: 8 + -5 + 8x + 22x + 2x2 = 5 + -22x + -5 + 22x Combine like terms: 8 + -5 = 3 3 + 8x + 22x + 2x2 = 5 + -22x + -5 + 22x Combine like terms: 8x + 22x = 30x 3 + 30x + 2x2 = 5 + -22x + -5 + 22x Reorder the terms: 3 + 30x + 2x2 = 5 + -5 + -22x + 22x Combine like terms: 5 + -5 = 0 3 + 30x + 2x2 = 0 + -22x + 22x 3 + 30x + 2x2 = -22x + 22x Combine like terms: -22x + 22x = 0 3 + 30x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 15x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 15x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 15x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 15x + x2 = 0 + -1.5 15x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 15x + x2 = -1.5 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -1.5 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -1.5 + 56.25 Combine like terms: -1.5 + 56.25 = 54.75 56.25 + 15x + x2 = 54.75 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 54.75 Calculate the square root of the right side: 7.399324293 Break this problem into two subproblems by setting (x + 7.5) equal to 7.399324293 and -7.399324293.Subproblem 1
x + 7.5 = 7.399324293 Simplifying x + 7.5 = 7.399324293 Reorder the terms: 7.5 + x = 7.399324293 Solving 7.5 + x = 7.399324293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 7.399324293 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.399324293 + -7.5 x = 7.399324293 + -7.5 Combine like terms: 7.399324293 + -7.5 = -0.100675707 x = -0.100675707 Simplifying x = -0.100675707Subproblem 2
x + 7.5 = -7.399324293 Simplifying x + 7.5 = -7.399324293 Reorder the terms: 7.5 + x = -7.399324293 Solving 7.5 + x = -7.399324293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -7.399324293 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.399324293 + -7.5 x = -7.399324293 + -7.5 Combine like terms: -7.399324293 + -7.5 = -14.899324293 x = -14.899324293 Simplifying x = -14.899324293Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.100675707, -14.899324293}
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