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Simplifying -0.9x2 + -3x = -0.3x2 + -38 Reorder the terms: -3x + -0.9x2 = -0.3x2 + -38 Reorder the terms: -3x + -0.9x2 = -38 + -0.3x2 Solving -3x + -0.9x2 = -38 + -0.3x2 Solving for variable 'x'. Reorder the terms: 38 + -3x + -0.9x2 + 0.3x2 = -38 + -0.3x2 + 38 + 0.3x2 Combine like terms: -0.9x2 + 0.3x2 = -0.6x2 38 + -3x + -0.6x2 = -38 + -0.3x2 + 38 + 0.3x2 Reorder the terms: 38 + -3x + -0.6x2 = -38 + 38 + -0.3x2 + 0.3x2 Combine like terms: -38 + 38 = 0 38 + -3x + -0.6x2 = 0 + -0.3x2 + 0.3x2 38 + -3x + -0.6x2 = -0.3x2 + 0.3x2 Combine like terms: -0.3x2 + 0.3x2 = 0.0 38 + -3x + -0.6x2 = 0.0 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. -63.33333333 + 5x + x2 = 0 Move the constant term to the right: Add '63.33333333' to each side of the equation. -63.33333333 + 5x + 63.33333333 + x2 = 0 + 63.33333333 Reorder the terms: -63.33333333 + 63.33333333 + 5x + x2 = 0 + 63.33333333 Combine like terms: -63.33333333 + 63.33333333 = 0.00000000 0.00000000 + 5x + x2 = 0 + 63.33333333 5x + x2 = 0 + 63.33333333 Combine like terms: 0 + 63.33333333 = 63.33333333 5x + x2 = 63.33333333 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 63.33333333 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 63.33333333 + 6.25 Combine like terms: 63.33333333 + 6.25 = 69.58333333 6.25 + 5x + x2 = 69.58333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 69.58333333 Calculate the square root of the right side: 8.341662504 Break this problem into two subproblems by setting (x + 2.5) equal to 8.341662504 and -8.341662504.Subproblem 1
x + 2.5 = 8.341662504 Simplifying x + 2.5 = 8.341662504 Reorder the terms: 2.5 + x = 8.341662504 Solving 2.5 + x = 8.341662504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 8.341662504 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 8.341662504 + -2.5 x = 8.341662504 + -2.5 Combine like terms: 8.341662504 + -2.5 = 5.841662504 x = 5.841662504 Simplifying x = 5.841662504Subproblem 2
x + 2.5 = -8.341662504 Simplifying x + 2.5 = -8.341662504 Reorder the terms: 2.5 + x = -8.341662504 Solving 2.5 + x = -8.341662504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -8.341662504 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -8.341662504 + -2.5 x = -8.341662504 + -2.5 Combine like terms: -8.341662504 + -2.5 = -10.841662504 x = -10.841662504 Simplifying x = -10.841662504Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.841662504, -10.841662504}
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