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Simplifying x2 + 18x + -84 = 0 Reorder the terms: -84 + 18x + x2 = 0 Solving -84 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 18x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 18x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 18x + x2 = 0 + 84 18x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 18x + x2 = 84 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 = 84 + 81 Reorder the terms: 81 + 18x + x2 = 84 + 81 Combine like terms: 84 + 81 = 165 81 + 18x + x2 = 165 Factor a perfect square on the left side: (x + 9)(x + 9) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (x + 9) equal to 12.845232579 and -12.845232579.Subproblem 1
x + 9 = 12.845232579 Simplifying x + 9 = 12.845232579 Reorder the terms: 9 + x = 12.845232579 Solving 9 + x = 12.845232579 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 = 12.845232579 + -9 Combine like terms: 9 + -9 = 0 0 + x = 12.845232579 + -9 x = 12.845232579 + -9 Combine like terms: 12.845232579 + -9 = 3.845232579 x = 3.845232579 Simplifying x = 3.845232579Subproblem 2
x + 9 = -12.845232579 Simplifying x + 9 = -12.845232579 Reorder the terms: 9 + x = -12.845232579 Solving 9 + x = -12.845232579 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 = -12.845232579 + -9 Combine like terms: 9 + -9 = 0 0 + x = -12.845232579 + -9 x = -12.845232579 + -9 Combine like terms: -12.845232579 + -9 = -21.845232579 x = -21.845232579 Simplifying x = -21.845232579Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.845232579, -21.845232579}
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