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Simplifying (15 + -2x)(x + 7) = 38 Reorder the terms: (15 + -2x)(7 + x) = 38 Multiply (15 + -2x) * (7 + x) (15(7 + x) + -2x * (7 + x)) = 38 ((7 * 15 + x * 15) + -2x * (7 + x)) = 38 ((105 + 15x) + -2x * (7 + x)) = 38 (105 + 15x + (7 * -2x + x * -2x)) = 38 (105 + 15x + (-14x + -2x2)) = 38 Combine like terms: 15x + -14x = 1x (105 + 1x + -2x2) = 38 Solving 105 + 1x + -2x2 = 38 Solving for variable 'x'. Reorder the terms: 105 + -38 + 1x + -2x2 = 38 + -38 Combine like terms: 105 + -38 = 67 67 + 1x + -2x2 = 38 + -38 Combine like terms: 38 + -38 = 0 67 + 1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -33.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '33.5' to each side of the equation. -33.5 + -0.5x + 33.5 + x2 = 0 + 33.5 Reorder the terms: -33.5 + 33.5 + -0.5x + x2 = 0 + 33.5 Combine like terms: -33.5 + 33.5 = 0.0 0.0 + -0.5x + x2 = 0 + 33.5 -0.5x + x2 = 0 + 33.5 Combine like terms: 0 + 33.5 = 33.5 -0.5x + x2 = 33.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 33.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 33.5 + 0.0625 Combine like terms: 33.5 + 0.0625 = 33.5625 0.0625 + -0.5x + x2 = 33.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 33.5625 Calculate the square root of the right side: 5.793315113 Break this problem into two subproblems by setting (x + -0.25) equal to 5.793315113 and -5.793315113.Subproblem 1
x + -0.25 = 5.793315113 Simplifying x + -0.25 = 5.793315113 Reorder the terms: -0.25 + x = 5.793315113 Solving -0.25 + x = 5.793315113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 5.793315113 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 5.793315113 + 0.25 x = 5.793315113 + 0.25 Combine like terms: 5.793315113 + 0.25 = 6.043315113 x = 6.043315113 Simplifying x = 6.043315113Subproblem 2
x + -0.25 = -5.793315113 Simplifying x + -0.25 = -5.793315113 Reorder the terms: -0.25 + x = -5.793315113 Solving -0.25 + x = -5.793315113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -5.793315113 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -5.793315113 + 0.25 x = -5.793315113 + 0.25 Combine like terms: -5.793315113 + 0.25 = -5.543315113 x = -5.543315113 Simplifying x = -5.543315113Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.043315113, -5.543315113}
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