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Simplifying x2 + 10.8x + -55.55 = 0 Reorder the terms: -55.55 + 10.8x + x2 = 0 Solving -55.55 + 10.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '55.55' to each side of the equation. -55.55 + 10.8x + 55.55 + x2 = 0 + 55.55 Reorder the terms: -55.55 + 55.55 + 10.8x + x2 = 0 + 55.55 Combine like terms: -55.55 + 55.55 = 0.00 0.00 + 10.8x + x2 = 0 + 55.55 10.8x + x2 = 0 + 55.55 Combine like terms: 0 + 55.55 = 55.55 10.8x + x2 = 55.55 The x term is 10.8x. Take half its coefficient (5.4). Square it (29.16) and add it to both sides. Add '29.16' to each side of the equation. 10.8x + 29.16 + x2 = 55.55 + 29.16 Reorder the terms: 29.16 + 10.8x + x2 = 55.55 + 29.16 Combine like terms: 55.55 + 29.16 = 84.71 29.16 + 10.8x + x2 = 84.71 Factor a perfect square on the left side: (x + 5.4)(x + 5.4) = 84.71 Calculate the square root of the right side: 9.203803562 Break this problem into two subproblems by setting (x + 5.4) equal to 9.203803562 and -9.203803562.Subproblem 1
x + 5.4 = 9.203803562 Simplifying x + 5.4 = 9.203803562 Reorder the terms: 5.4 + x = 9.203803562 Solving 5.4 + x = 9.203803562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.4' to each side of the equation. 5.4 + -5.4 + x = 9.203803562 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + x = 9.203803562 + -5.4 x = 9.203803562 + -5.4 Combine like terms: 9.203803562 + -5.4 = 3.803803562 x = 3.803803562 Simplifying x = 3.803803562Subproblem 2
x + 5.4 = -9.203803562 Simplifying x + 5.4 = -9.203803562 Reorder the terms: 5.4 + x = -9.203803562 Solving 5.4 + x = -9.203803562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.4' to each side of the equation. 5.4 + -5.4 + x = -9.203803562 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + x = -9.203803562 + -5.4 x = -9.203803562 + -5.4 Combine like terms: -9.203803562 + -5.4 = -14.603803562 x = -14.603803562 Simplifying x = -14.603803562Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.803803562, -14.603803562}
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