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Simplifying x2 + -66x + 7 = 0 Reorder the terms: 7 + -66x + x2 = 0 Solving 7 + -66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -66x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -66x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -66x + x2 = 0 + -7 -66x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -66x + x2 = -7 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 = -7 + 1089 Reorder the terms: 1089 + -66x + x2 = -7 + 1089 Combine like terms: -7 + 1089 = 1082 1089 + -66x + x2 = 1082 Factor a perfect square on the left side: (x + -33)(x + -33) = 1082 Calculate the square root of the right side: 32.893768407 Break this problem into two subproblems by setting (x + -33) equal to 32.893768407 and -32.893768407.Subproblem 1
x + -33 = 32.893768407 Simplifying x + -33 = 32.893768407 Reorder the terms: -33 + x = 32.893768407 Solving -33 + x = 32.893768407 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 = 32.893768407 + 33 Combine like terms: -33 + 33 = 0 0 + x = 32.893768407 + 33 x = 32.893768407 + 33 Combine like terms: 32.893768407 + 33 = 65.893768407 x = 65.893768407 Simplifying x = 65.893768407Subproblem 2
x + -33 = -32.893768407 Simplifying x + -33 = -32.893768407 Reorder the terms: -33 + x = -32.893768407 Solving -33 + x = -32.893768407 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 = -32.893768407 + 33 Combine like terms: -33 + 33 = 0 0 + x = -32.893768407 + 33 x = -32.893768407 + 33 Combine like terms: -32.893768407 + 33 = 0.106231593 x = 0.106231593 Simplifying x = 0.106231593Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.893768407, 0.106231593}
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