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Simplifying -2.8x2 + 3.1x = -0.5 Reorder the terms: 3.1x + -2.8x2 = -0.5 Solving 3.1x + -2.8x2 = -0.5 Solving for variable 'x'. Reorder the terms: 0.5 + 3.1x + -2.8x2 = -0.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.5 + 3.1x + -2.8x2 = 0.0 Begin completing the square. Divide all terms by -2.8 the coefficient of the squared term: Divide each side by '-2.8'. -0.1785714286 + -1.107142857x + x2 = 0 Move the constant term to the right: Add '0.1785714286' to each side of the equation. -0.1785714286 + -1.107142857x + 0.1785714286 + x2 = 0 + 0.1785714286 Reorder the terms: -0.1785714286 + 0.1785714286 + -1.107142857x + x2 = 0 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + -1.107142857x + x2 = 0 + 0.1785714286 -1.107142857x + x2 = 0 + 0.1785714286 Combine like terms: 0 + 0.1785714286 = 0.1785714286 -1.107142857x + x2 = 0.1785714286 The x term is -1.107142857x. Take half its coefficient (-0.5535714285). Square it (0.3064413265) and add it to both sides. Add '0.3064413265' to each side of the equation. -1.107142857x + 0.3064413265 + x2 = 0.1785714286 + 0.3064413265 Reorder the terms: 0.3064413265 + -1.107142857x + x2 = 0.1785714286 + 0.3064413265 Combine like terms: 0.1785714286 + 0.3064413265 = 0.4850127551 0.3064413265 + -1.107142857x + x2 = 0.4850127551 Factor a perfect square on the left side: (x + -0.5535714285)(x + -0.5535714285) = 0.4850127551 Calculate the square root of the right side: 0.696428571 Break this problem into two subproblems by setting (x + -0.5535714285) equal to 0.696428571 and -0.696428571.Subproblem 1
x + -0.5535714285 = 0.696428571 Simplifying x + -0.5535714285 = 0.696428571 Reorder the terms: -0.5535714285 + x = 0.696428571 Solving -0.5535714285 + x = 0.696428571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5535714285' to each side of the equation. -0.5535714285 + 0.5535714285 + x = 0.696428571 + 0.5535714285 Combine like terms: -0.5535714285 + 0.5535714285 = 0.0000000000 0.0000000000 + x = 0.696428571 + 0.5535714285 x = 0.696428571 + 0.5535714285 Combine like terms: 0.696428571 + 0.5535714285 = 1.2499999995 x = 1.2499999995 Simplifying x = 1.2499999995Subproblem 2
x + -0.5535714285 = -0.696428571 Simplifying x + -0.5535714285 = -0.696428571 Reorder the terms: -0.5535714285 + x = -0.696428571 Solving -0.5535714285 + x = -0.696428571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5535714285' to each side of the equation. -0.5535714285 + 0.5535714285 + x = -0.696428571 + 0.5535714285 Combine like terms: -0.5535714285 + 0.5535714285 = 0.0000000000 0.0000000000 + x = -0.696428571 + 0.5535714285 x = -0.696428571 + 0.5535714285 Combine like terms: -0.696428571 + 0.5535714285 = -0.1428571425 x = -0.1428571425 Simplifying x = -0.1428571425Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2499999995, -0.1428571425}
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