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Simplifying x2 + 8.544x + -13.5 = 0 Reorder the terms: -13.5 + 8.544x + x2 = 0 Solving -13.5 + 8.544x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 8.544x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 8.544x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 8.544x + x2 = 0 + 13.5 8.544x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 8.544x + x2 = 13.5 The x term is 8.544x. Take half its coefficient (4.272). Square it (18.249984) and add it to both sides. Add '18.249984' to each side of the equation. 8.544x + 18.249984 + x2 = 13.5 + 18.249984 Reorder the terms: 18.249984 + 8.544x + x2 = 13.5 + 18.249984 Combine like terms: 13.5 + 18.249984 = 31.749984 18.249984 + 8.544x + x2 = 31.749984 Factor a perfect square on the left side: (x + 4.272)(x + 4.272) = 31.749984 Calculate the square root of the right side: 5.634712415 Break this problem into two subproblems by setting (x + 4.272) equal to 5.634712415 and -5.634712415.Subproblem 1
x + 4.272 = 5.634712415 Simplifying x + 4.272 = 5.634712415 Reorder the terms: 4.272 + x = 5.634712415 Solving 4.272 + x = 5.634712415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.272' to each side of the equation. 4.272 + -4.272 + x = 5.634712415 + -4.272 Combine like terms: 4.272 + -4.272 = 0.000 0.000 + x = 5.634712415 + -4.272 x = 5.634712415 + -4.272 Combine like terms: 5.634712415 + -4.272 = 1.362712415 x = 1.362712415 Simplifying x = 1.362712415Subproblem 2
x + 4.272 = -5.634712415 Simplifying x + 4.272 = -5.634712415 Reorder the terms: 4.272 + x = -5.634712415 Solving 4.272 + x = -5.634712415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.272' to each side of the equation. 4.272 + -4.272 + x = -5.634712415 + -4.272 Combine like terms: 4.272 + -4.272 = 0.000 0.000 + x = -5.634712415 + -4.272 x = -5.634712415 + -4.272 Combine like terms: -5.634712415 + -4.272 = -9.906712415 x = -9.906712415 Simplifying x = -9.906712415Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.362712415, -9.906712415}
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