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Simplifying -4.905x2 + -1.3x + 27 = 0 Reorder the terms: 27 + -1.3x + -4.905x2 = 0 Solving 27 + -1.3x + -4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -5.504587156 + 0.2650356779x + x2 = 0 Move the constant term to the right: Add '5.504587156' to each side of the equation. -5.504587156 + 0.2650356779x + 5.504587156 + x2 = 0 + 5.504587156 Reorder the terms: -5.504587156 + 5.504587156 + 0.2650356779x + x2 = 0 + 5.504587156 Combine like terms: -5.504587156 + 5.504587156 = 0.000000000 0.000000000 + 0.2650356779x + x2 = 0 + 5.504587156 0.2650356779x + x2 = 0 + 5.504587156 Combine like terms: 0 + 5.504587156 = 5.504587156 0.2650356779x + x2 = 5.504587156 The x term is 0.2650356779x. Take half its coefficient (0.132517839). Square it (0.01756097765) and add it to both sides. Add '0.01756097765' to each side of the equation. 0.2650356779x + 0.01756097765 + x2 = 5.504587156 + 0.01756097765 Reorder the terms: 0.01756097765 + 0.2650356779x + x2 = 5.504587156 + 0.01756097765 Combine like terms: 5.504587156 + 0.01756097765 = 5.52214813365 0.01756097765 + 0.2650356779x + x2 = 5.52214813365 Factor a perfect square on the left side: (x + 0.132517839)(x + 0.132517839) = 5.52214813365 Calculate the square root of the right side: 2.349925134 Break this problem into two subproblems by setting (x + 0.132517839) equal to 2.349925134 and -2.349925134.Subproblem 1
x + 0.132517839 = 2.349925134 Simplifying x + 0.132517839 = 2.349925134 Reorder the terms: 0.132517839 + x = 2.349925134 Solving 0.132517839 + x = 2.349925134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.132517839' to each side of the equation. 0.132517839 + -0.132517839 + x = 2.349925134 + -0.132517839 Combine like terms: 0.132517839 + -0.132517839 = 0.000000000 0.000000000 + x = 2.349925134 + -0.132517839 x = 2.349925134 + -0.132517839 Combine like terms: 2.349925134 + -0.132517839 = 2.217407295 x = 2.217407295 Simplifying x = 2.217407295Subproblem 2
x + 0.132517839 = -2.349925134 Simplifying x + 0.132517839 = -2.349925134 Reorder the terms: 0.132517839 + x = -2.349925134 Solving 0.132517839 + x = -2.349925134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.132517839' to each side of the equation. 0.132517839 + -0.132517839 + x = -2.349925134 + -0.132517839 Combine like terms: 0.132517839 + -0.132517839 = 0.000000000 0.000000000 + x = -2.349925134 + -0.132517839 x = -2.349925134 + -0.132517839 Combine like terms: -2.349925134 + -0.132517839 = -2.482442973 x = -2.482442973 Simplifying x = -2.482442973Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.217407295, -2.482442973}
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