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Simplifying x2 + -18x + -53 = -6 Reorder the terms: -53 + -18x + x2 = -6 Solving -53 + -18x + x2 = -6 Solving for variable 'x'. Reorder the terms: -53 + 6 + -18x + x2 = -6 + 6 Combine like terms: -53 + 6 = -47 -47 + -18x + x2 = -6 + 6 Combine like terms: -6 + 6 = 0 -47 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -18x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + -18x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -18x + x2 = 0 + 47 -18x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 -18x + x2 = 47 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 47 + 81 Reorder the terms: 81 + -18x + x2 = 47 + 81 Combine like terms: 47 + 81 = 128 81 + -18x + x2 = 128 Factor a perfect square on the left side: (x + -9)(x + -9) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + -9) equal to 11.313708499 and -11.313708499.Subproblem 1
x + -9 = 11.313708499 Simplifying x + -9 = 11.313708499 Reorder the terms: -9 + x = 11.313708499 Solving -9 + x = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 11.313708499 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11.313708499 + 9 x = 11.313708499 + 9 Combine like terms: 11.313708499 + 9 = 20.313708499 x = 20.313708499 Simplifying x = 20.313708499Subproblem 2
x + -9 = -11.313708499 Simplifying x + -9 = -11.313708499 Reorder the terms: -9 + x = -11.313708499 Solving -9 + x = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -11.313708499 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11.313708499 + 9 x = -11.313708499 + 9 Combine like terms: -11.313708499 + 9 = -2.313708499 x = -2.313708499 Simplifying x = -2.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.313708499, -2.313708499}
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