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Simplifying x(x + 76) = 768 Reorder the terms: x(76 + x) = 768 (76 * x + x * x) = 768 (76x + x2) = 768 Solving 76x + x2 = 768 Solving for variable 'x'. Reorder the terms: -768 + 76x + x2 = 768 + -768 Combine like terms: 768 + -768 = 0 -768 + 76x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '768' to each side of the equation. -768 + 76x + 768 + x2 = 0 + 768 Reorder the terms: -768 + 768 + 76x + x2 = 0 + 768 Combine like terms: -768 + 768 = 0 0 + 76x + x2 = 0 + 768 76x + x2 = 0 + 768 Combine like terms: 0 + 768 = 768 76x + x2 = 768 The x term is 76x. Take half its coefficient (38). Square it (1444) and add it to both sides. Add '1444' to each side of the equation. 76x + 1444 + x2 = 768 + 1444 Reorder the terms: 1444 + 76x + x2 = 768 + 1444 Combine like terms: 768 + 1444 = 2212 1444 + 76x + x2 = 2212 Factor a perfect square on the left side: (x + 38)(x + 38) = 2212 Calculate the square root of the right side: 47.031904065 Break this problem into two subproblems by setting (x + 38) equal to 47.031904065 and -47.031904065.Subproblem 1
x + 38 = 47.031904065 Simplifying x + 38 = 47.031904065 Reorder the terms: 38 + x = 47.031904065 Solving 38 + x = 47.031904065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = 47.031904065 + -38 Combine like terms: 38 + -38 = 0 0 + x = 47.031904065 + -38 x = 47.031904065 + -38 Combine like terms: 47.031904065 + -38 = 9.031904065 x = 9.031904065 Simplifying x = 9.031904065Subproblem 2
x + 38 = -47.031904065 Simplifying x + 38 = -47.031904065 Reorder the terms: 38 + x = -47.031904065 Solving 38 + x = -47.031904065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = -47.031904065 + -38 Combine like terms: 38 + -38 = 0 0 + x = -47.031904065 + -38 x = -47.031904065 + -38 Combine like terms: -47.031904065 + -38 = -85.031904065 x = -85.031904065 Simplifying x = -85.031904065Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.031904065, -85.031904065}
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