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Simplifying x2 + 66x + 10 = 0 Reorder the terms: 10 + 66x + x2 = 0 Solving 10 + 66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 66x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 66x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 66x + x2 = 0 + -10 66x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 66x + x2 = -10 The x term is 66x. Take half its coefficient (33). Square it (1089) and add it to both sides. Add '1089' to each side of the equation. 66x + 1089 + x2 = -10 + 1089 Reorder the terms: 1089 + 66x + x2 = -10 + 1089 Combine like terms: -10 + 1089 = 1079 1089 + 66x + x2 = 1079 Factor a perfect square on the left side: (x + 33)(x + 33) = 1079 Calculate the square root of the right side: 32.848135411 Break this problem into two subproblems by setting (x + 33) equal to 32.848135411 and -32.848135411.Subproblem 1
x + 33 = 32.848135411 Simplifying x + 33 = 32.848135411 Reorder the terms: 33 + x = 32.848135411 Solving 33 + x = 32.848135411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + x = 32.848135411 + -33 Combine like terms: 33 + -33 = 0 0 + x = 32.848135411 + -33 x = 32.848135411 + -33 Combine like terms: 32.848135411 + -33 = -0.151864589 x = -0.151864589 Simplifying x = -0.151864589Subproblem 2
x + 33 = -32.848135411 Simplifying x + 33 = -32.848135411 Reorder the terms: 33 + x = -32.848135411 Solving 33 + x = -32.848135411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + x = -32.848135411 + -33 Combine like terms: 33 + -33 = 0 0 + x = -32.848135411 + -33 x = -32.848135411 + -33 Combine like terms: -32.848135411 + -33 = -65.848135411 x = -65.848135411 Simplifying x = -65.848135411Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.151864589, -65.848135411}
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