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Simplifying x2 + 58x + -38 = 0 Reorder the terms: -38 + 58x + x2 = 0 Solving -38 + 58x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 58x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + 58x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 58x + x2 = 0 + 38 58x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 58x + x2 = 38 The x term is 58x. Take half its coefficient (29). Square it (841) and add it to both sides. Add '841' to each side of the equation. 58x + 841 + x2 = 38 + 841 Reorder the terms: 841 + 58x + x2 = 38 + 841 Combine like terms: 38 + 841 = 879 841 + 58x + x2 = 879 Factor a perfect square on the left side: (x + 29)(x + 29) = 879 Calculate the square root of the right side: 29.647934161 Break this problem into two subproblems by setting (x + 29) equal to 29.647934161 and -29.647934161.Subproblem 1
x + 29 = 29.647934161 Simplifying x + 29 = 29.647934161 Reorder the terms: 29 + x = 29.647934161 Solving 29 + x = 29.647934161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = 29.647934161 + -29 Combine like terms: 29 + -29 = 0 0 + x = 29.647934161 + -29 x = 29.647934161 + -29 Combine like terms: 29.647934161 + -29 = 0.647934161 x = 0.647934161 Simplifying x = 0.647934161Subproblem 2
x + 29 = -29.647934161 Simplifying x + 29 = -29.647934161 Reorder the terms: 29 + x = -29.647934161 Solving 29 + x = -29.647934161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = -29.647934161 + -29 Combine like terms: 29 + -29 = 0 0 + x = -29.647934161 + -29 x = -29.647934161 + -29 Combine like terms: -29.647934161 + -29 = -58.647934161 x = -58.647934161 Simplifying x = -58.647934161Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.647934161, -58.647934161}
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