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Simplifying (x + -16)(3x + 8) = 400 Reorder the terms: (-16 + x)(3x + 8) = 400 Reorder the terms: (-16 + x)(8 + 3x) = 400 Multiply (-16 + x) * (8 + 3x) (-16(8 + 3x) + x(8 + 3x)) = 400 ((8 * -16 + 3x * -16) + x(8 + 3x)) = 400 ((-128 + -48x) + x(8 + 3x)) = 400 (-128 + -48x + (8 * x + 3x * x)) = 400 (-128 + -48x + (8x + 3x2)) = 400 Combine like terms: -48x + 8x = -40x (-128 + -40x + 3x2) = 400 Solving -128 + -40x + 3x2 = 400 Solving for variable 'x'. Reorder the terms: -128 + -400 + -40x + 3x2 = 400 + -400 Combine like terms: -128 + -400 = -528 -528 + -40x + 3x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -528 + -40x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -176 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '176' to each side of the equation. -176 + -13.33333333x + 176 + x2 = 0 + 176 Reorder the terms: -176 + 176 + -13.33333333x + x2 = 0 + 176 Combine like terms: -176 + 176 = 0 0 + -13.33333333x + x2 = 0 + 176 -13.33333333x + x2 = 0 + 176 Combine like terms: 0 + 176 = 176 -13.33333333x + x2 = 176 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = 176 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = 176 + 44.44444442 Combine like terms: 176 + 44.44444442 = 220.44444442 44.44444442 + -13.33333333x + x2 = 220.44444442 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 220.44444442 Calculate the square root of the right side: 14.847371633 Break this problem into two subproblems by setting (x + -6.666666665) equal to 14.847371633 and -14.847371633.Subproblem 1
x + -6.666666665 = 14.847371633 Simplifying x + -6.666666665 = 14.847371633 Reorder the terms: -6.666666665 + x = 14.847371633 Solving -6.666666665 + x = 14.847371633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 14.847371633 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 14.847371633 + 6.666666665 x = 14.847371633 + 6.666666665 Combine like terms: 14.847371633 + 6.666666665 = 21.514038298 x = 21.514038298 Simplifying x = 21.514038298Subproblem 2
x + -6.666666665 = -14.847371633 Simplifying x + -6.666666665 = -14.847371633 Reorder the terms: -6.666666665 + x = -14.847371633 Solving -6.666666665 + x = -14.847371633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -14.847371633 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -14.847371633 + 6.666666665 x = -14.847371633 + 6.666666665 Combine like terms: -14.847371633 + 6.666666665 = -8.180704968 x = -8.180704968 Simplifying x = -8.180704968Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.514038298, -8.180704968}
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