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Simplifying x2 + -6x + 9 = 62.7 Reorder the terms: 9 + -6x + x2 = 62.7 Solving 9 + -6x + x2 = 62.7 Solving for variable 'x'. Reorder the terms: 9 + -62.7 + -6x + x2 = 62.7 + -62.7 Combine like terms: 9 + -62.7 = -53.7 -53.7 + -6x + x2 = 62.7 + -62.7 Combine like terms: 62.7 + -62.7 = 0.0 -53.7 + -6x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '53.7' to each side of the equation. -53.7 + -6x + 53.7 + x2 = 0.0 + 53.7 Reorder the terms: -53.7 + 53.7 + -6x + x2 = 0.0 + 53.7 Combine like terms: -53.7 + 53.7 = 0.0 0.0 + -6x + x2 = 0.0 + 53.7 -6x + x2 = 0.0 + 53.7 Combine like terms: 0.0 + 53.7 = 53.7 -6x + x2 = 53.7 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 53.7 + 9 Reorder the terms: 9 + -6x + x2 = 53.7 + 9 Combine like terms: 53.7 + 9 = 62.7 9 + -6x + x2 = 62.7 Factor a perfect square on the left side: (x + -3)(x + -3) = 62.7 Calculate the square root of the right side: 7.918333158 Break this problem into two subproblems by setting (x + -3) equal to 7.918333158 and -7.918333158.Subproblem 1
x + -3 = 7.918333158 Simplifying x + -3 = 7.918333158 Reorder the terms: -3 + x = 7.918333158 Solving -3 + x = 7.918333158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 7.918333158 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.918333158 + 3 x = 7.918333158 + 3 Combine like terms: 7.918333158 + 3 = 10.918333158 x = 10.918333158 Simplifying x = 10.918333158Subproblem 2
x + -3 = -7.918333158 Simplifying x + -3 = -7.918333158 Reorder the terms: -3 + x = -7.918333158 Solving -3 + x = -7.918333158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -7.918333158 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.918333158 + 3 x = -7.918333158 + 3 Combine like terms: -7.918333158 + 3 = -4.918333158 x = -4.918333158 Simplifying x = -4.918333158Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.918333158, -4.918333158}
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