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Simplifying x2 + 12.6x + -216.31 = 0 Reorder the terms: -216.31 + 12.6x + x2 = 0 Solving -216.31 + 12.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '216.31' to each side of the equation. -216.31 + 12.6x + 216.31 + x2 = 0 + 216.31 Reorder the terms: -216.31 + 216.31 + 12.6x + x2 = 0 + 216.31 Combine like terms: -216.31 + 216.31 = 0.00 0.00 + 12.6x + x2 = 0 + 216.31 12.6x + x2 = 0 + 216.31 Combine like terms: 0 + 216.31 = 216.31 12.6x + x2 = 216.31 The x term is 12.6x. Take half its coefficient (6.3). Square it (39.69) and add it to both sides. Add '39.69' to each side of the equation. 12.6x + 39.69 + x2 = 216.31 + 39.69 Reorder the terms: 39.69 + 12.6x + x2 = 216.31 + 39.69 Combine like terms: 216.31 + 39.69 = 256 39.69 + 12.6x + x2 = 256 Factor a perfect square on the left side: (x + 6.3)(x + 6.3) = 256 Calculate the square root of the right side: 16 Break this problem into two subproblems by setting (x + 6.3) equal to 16 and -16.Subproblem 1
x + 6.3 = 16 Simplifying x + 6.3 = 16 Reorder the terms: 6.3 + x = 16 Solving 6.3 + x = 16 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.3' to each side of the equation. 6.3 + -6.3 + x = 16 + -6.3 Combine like terms: 6.3 + -6.3 = 0.0 0.0 + x = 16 + -6.3 x = 16 + -6.3 Combine like terms: 16 + -6.3 = 9.7 x = 9.7 Simplifying x = 9.7Subproblem 2
x + 6.3 = -16 Simplifying x + 6.3 = -16 Reorder the terms: 6.3 + x = -16 Solving 6.3 + x = -16 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.3' to each side of the equation. 6.3 + -6.3 + x = -16 + -6.3 Combine like terms: 6.3 + -6.3 = 0.0 0.0 + x = -16 + -6.3 x = -16 + -6.3 Combine like terms: -16 + -6.3 = -22.3 x = -22.3 Simplifying x = -22.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.7, -22.3}
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