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Simplifying (x + -2)(x + 5) = 400 Reorder the terms: (-2 + x)(x + 5) = 400 Reorder the terms: (-2 + x)(5 + x) = 400 Multiply (-2 + x) * (5 + x) (-2(5 + x) + x(5 + x)) = 400 ((5 * -2 + x * -2) + x(5 + x)) = 400 ((-10 + -2x) + x(5 + x)) = 400 (-10 + -2x + (5 * x + x * x)) = 400 (-10 + -2x + (5x + x2)) = 400 Combine like terms: -2x + 5x = 3x (-10 + 3x + x2) = 400 Solving -10 + 3x + x2 = 400 Solving for variable 'x'. Reorder the terms: -10 + -400 + 3x + x2 = 400 + -400 Combine like terms: -10 + -400 = -410 -410 + 3x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -410 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '410' to each side of the equation. -410 + 3x + 410 + x2 = 0 + 410 Reorder the terms: -410 + 410 + 3x + x2 = 0 + 410 Combine like terms: -410 + 410 = 0 0 + 3x + x2 = 0 + 410 3x + x2 = 0 + 410 Combine like terms: 0 + 410 = 410 3x + x2 = 410 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 410 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 410 + 2.25 Combine like terms: 410 + 2.25 = 412.25 2.25 + 3x + x2 = 412.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 412.25 Calculate the square root of the right side: 20.303940504 Break this problem into two subproblems by setting (x + 1.5) equal to 20.303940504 and -20.303940504.Subproblem 1
x + 1.5 = 20.303940504 Simplifying x + 1.5 = 20.303940504 Reorder the terms: 1.5 + x = 20.303940504 Solving 1.5 + x = 20.303940504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 20.303940504 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 20.303940504 + -1.5 x = 20.303940504 + -1.5 Combine like terms: 20.303940504 + -1.5 = 18.803940504 x = 18.803940504 Simplifying x = 18.803940504Subproblem 2
x + 1.5 = -20.303940504 Simplifying x + 1.5 = -20.303940504 Reorder the terms: 1.5 + x = -20.303940504 Solving 1.5 + x = -20.303940504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -20.303940504 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -20.303940504 + -1.5 x = -20.303940504 + -1.5 Combine like terms: -20.303940504 + -1.5 = -21.803940504 x = -21.803940504 Simplifying x = -21.803940504Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.803940504, -21.803940504}
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