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Simplifying x2 + 18x + -62.388737692 = 0 Reorder the terms: -62.388737692 + 18x + x2 = 0 Solving -62.388737692 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '62.388737692' to each side of the equation. -62.388737692 + 18x + 62.388737692 + x2 = 0 + 62.388737692 Reorder the terms: -62.388737692 + 62.388737692 + 18x + x2 = 0 + 62.388737692 Combine like terms: -62.388737692 + 62.388737692 = 0.000000000 0.000000000 + 18x + x2 = 0 + 62.388737692 18x + x2 = 0 + 62.388737692 Combine like terms: 0 + 62.388737692 = 62.388737692 18x + x2 = 62.388737692 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 = 62.388737692 + 81 Reorder the terms: 81 + 18x + x2 = 62.388737692 + 81 Combine like terms: 62.388737692 + 81 = 143.388737692 81 + 18x + x2 = 143.388737692 Factor a perfect square on the left side: (x + 9)(x + 9) = 143.388737692 Calculate the square root of the right side: 11.974503651 Break this problem into two subproblems by setting (x + 9) equal to 11.974503651 and -11.974503651.Subproblem 1
x + 9 = 11.974503651 Simplifying x + 9 = 11.974503651 Reorder the terms: 9 + x = 11.974503651 Solving 9 + x = 11.974503651 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 = 11.974503651 + -9 Combine like terms: 9 + -9 = 0 0 + x = 11.974503651 + -9 x = 11.974503651 + -9 Combine like terms: 11.974503651 + -9 = 2.974503651 x = 2.974503651 Simplifying x = 2.974503651Subproblem 2
x + 9 = -11.974503651 Simplifying x + 9 = -11.974503651 Reorder the terms: 9 + x = -11.974503651 Solving 9 + x = -11.974503651 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 = -11.974503651 + -9 Combine like terms: 9 + -9 = 0 0 + x = -11.974503651 + -9 x = -11.974503651 + -9 Combine like terms: -11.974503651 + -9 = -20.974503651 x = -20.974503651 Simplifying x = -20.974503651Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.974503651, -20.974503651}
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