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Simplifying x2 + 18x = -38 Reorder the terms: 18x + x2 = -38 Solving 18x + x2 = -38 Solving for variable 'x'. Reorder the terms: 38 + 18x + x2 = -38 + 38 Combine like terms: -38 + 38 = 0 38 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + 18x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + 18x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 18x + x2 = 0 + -38 18x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 18x + x2 = -38 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 = -38 + 81 Reorder the terms: 81 + 18x + x2 = -38 + 81 Combine like terms: -38 + 81 = 43 81 + 18x + x2 = 43 Factor a perfect square on the left side: (x + 9)(x + 9) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + 9) equal to 6.557438524 and -6.557438524.Subproblem 1
x + 9 = 6.557438524 Simplifying x + 9 = 6.557438524 Reorder the terms: 9 + x = 6.557438524 Solving 9 + x = 6.557438524 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 = 6.557438524 + -9 Combine like terms: 9 + -9 = 0 0 + x = 6.557438524 + -9 x = 6.557438524 + -9 Combine like terms: 6.557438524 + -9 = -2.442561476 x = -2.442561476 Simplifying x = -2.442561476Subproblem 2
x + 9 = -6.557438524 Simplifying x + 9 = -6.557438524 Reorder the terms: 9 + x = -6.557438524 Solving 9 + x = -6.557438524 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 = -6.557438524 + -9 Combine like terms: 9 + -9 = 0 0 + x = -6.557438524 + -9 x = -6.557438524 + -9 Combine like terms: -6.557438524 + -9 = -15.557438524 x = -15.557438524 Simplifying x = -15.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.442561476, -15.557438524}
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