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Simplifying x2 + 15 = 77x Reorder the terms: 15 + x2 = 77x Solving 15 + x2 = 77x Solving for variable 'x'. Reorder the terms: 15 + -77x + x2 = 77x + -77x Combine like terms: 77x + -77x = 0 15 + -77x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -77x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -77x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -77x + x2 = 0 + -15 -77x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -77x + x2 = -15 The x term is -77x. Take half its coefficient (-38.5). Square it (1482.25) and add it to both sides. Add '1482.25' to each side of the equation. -77x + 1482.25 + x2 = -15 + 1482.25 Reorder the terms: 1482.25 + -77x + x2 = -15 + 1482.25 Combine like terms: -15 + 1482.25 = 1467.25 1482.25 + -77x + x2 = 1467.25 Factor a perfect square on the left side: (x + -38.5)(x + -38.5) = 1467.25 Calculate the square root of the right side: 38.304699451 Break this problem into two subproblems by setting (x + -38.5) equal to 38.304699451 and -38.304699451.Subproblem 1
x + -38.5 = 38.304699451 Simplifying x + -38.5 = 38.304699451 Reorder the terms: -38.5 + x = 38.304699451 Solving -38.5 + x = 38.304699451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.5' to each side of the equation. -38.5 + 38.5 + x = 38.304699451 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + x = 38.304699451 + 38.5 x = 38.304699451 + 38.5 Combine like terms: 38.304699451 + 38.5 = 76.804699451 x = 76.804699451 Simplifying x = 76.804699451Subproblem 2
x + -38.5 = -38.304699451 Simplifying x + -38.5 = -38.304699451 Reorder the terms: -38.5 + x = -38.304699451 Solving -38.5 + x = -38.304699451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.5' to each side of the equation. -38.5 + 38.5 + x = -38.304699451 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + x = -38.304699451 + 38.5 x = -38.304699451 + 38.5 Combine like terms: -38.304699451 + 38.5 = 0.195300549 x = 0.195300549 Simplifying x = 0.195300549Solution
The solution to the problem is based on the solutions from the subproblems. x = {76.804699451, 0.195300549}
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