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Simplifying (18 + 2)(x + -4) = (x * x) + -1(32 * 32) Combine like terms: 18 + 2 = 20 (20)(x + -4) = (x * x) + -1(32 * 32) Reorder the terms: 20(-4 + x) = (x * x) + -1(32 * 32) (-4 * 20 + x * 20) = (x * x) + -1(32 * 32) (-80 + 20x) = (x * x) + -1(32 * 32) Multiply x * x -80 + 20x = (x2) + -1(32 * 32) -80 + 20x = x2 + -1(32 * 32) Multiply 32 * 32 -80 + 20x = x2 + -1(1024) Multiply -1 * 1024 -80 + 20x = x2 + -1024 Reorder the terms: -80 + 20x = -1024 + x2 Solving -80 + 20x = -1024 + x2 Solving for variable 'x'. Reorder the terms: -80 + 1024 + 20x + -1x2 = -1024 + x2 + 1024 + -1x2 Combine like terms: -80 + 1024 = 944 944 + 20x + -1x2 = -1024 + x2 + 1024 + -1x2 Reorder the terms: 944 + 20x + -1x2 = -1024 + 1024 + x2 + -1x2 Combine like terms: -1024 + 1024 = 0 944 + 20x + -1x2 = 0 + x2 + -1x2 944 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 944 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -944 + -20x + x2 = 0 Move the constant term to the right: Add '944' to each side of the equation. -944 + -20x + 944 + x2 = 0 + 944 Reorder the terms: -944 + 944 + -20x + x2 = 0 + 944 Combine like terms: -944 + 944 = 0 0 + -20x + x2 = 0 + 944 -20x + x2 = 0 + 944 Combine like terms: 0 + 944 = 944 -20x + x2 = 944 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 944 + 100 Reorder the terms: 100 + -20x + x2 = 944 + 100 Combine like terms: 944 + 100 = 1044 100 + -20x + x2 = 1044 Factor a perfect square on the left side: (x + -10)(x + -10) = 1044 Calculate the square root of the right side: 32.310988843 Break this problem into two subproblems by setting (x + -10) equal to 32.310988843 and -32.310988843.Subproblem 1
x + -10 = 32.310988843 Simplifying x + -10 = 32.310988843 Reorder the terms: -10 + x = 32.310988843 Solving -10 + x = 32.310988843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 32.310988843 + 10 Combine like terms: -10 + 10 = 0 0 + x = 32.310988843 + 10 x = 32.310988843 + 10 Combine like terms: 32.310988843 + 10 = 42.310988843 x = 42.310988843 Simplifying x = 42.310988843Subproblem 2
x + -10 = -32.310988843 Simplifying x + -10 = -32.310988843 Reorder the terms: -10 + x = -32.310988843 Solving -10 + x = -32.310988843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -32.310988843 + 10 Combine like terms: -10 + 10 = 0 0 + x = -32.310988843 + 10 x = -32.310988843 + 10 Combine like terms: -32.310988843 + 10 = -22.310988843 x = -22.310988843 Simplifying x = -22.310988843Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.310988843, -22.310988843}
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