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Simplifying (3 + -11x + -4x2) + -1(5x2 + 12x + -4) = 0 Remove parenthesis around (3 + -11x + -4x2) 3 + -11x + -4x2 + -1(5x2 + 12x + -4) = 0 Reorder the terms: 3 + -11x + -4x2 + -1(-4 + 12x + 5x2) = 0 3 + -11x + -4x2 + (-4 * -1 + 12x * -1 + 5x2 * -1) = 0 3 + -11x + -4x2 + (4 + -12x + -5x2) = 0 Reorder the terms: 3 + 4 + -11x + -12x + -4x2 + -5x2 = 0 Combine like terms: 3 + 4 = 7 7 + -11x + -12x + -4x2 + -5x2 = 0 Combine like terms: -11x + -12x = -23x 7 + -23x + -4x2 + -5x2 = 0 Combine like terms: -4x2 + -5x2 = -9x2 7 + -23x + -9x2 = 0 Solving 7 + -23x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.7777777778 + 2.555555556x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + 2.555555556x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + 2.555555556x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + 2.555555556x + x2 = 0 + 0.7777777778 2.555555556x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 2.555555556x + x2 = 0.7777777778 The x term is 2.555555556x. Take half its coefficient (1.277777778). Square it (1.632716050) and add it to both sides. Add '1.632716050' to each side of the equation. 2.555555556x + 1.632716050 + x2 = 0.7777777778 + 1.632716050 Reorder the terms: 1.632716050 + 2.555555556x + x2 = 0.7777777778 + 1.632716050 Combine like terms: 0.7777777778 + 1.632716050 = 2.4104938278 1.632716050 + 2.555555556x + x2 = 2.4104938278 Factor a perfect square on the left side: (x + 1.277777778)(x + 1.277777778) = 2.4104938278 Calculate the square root of the right side: 1.552576513 Break this problem into two subproblems by setting (x + 1.277777778) equal to 1.552576513 and -1.552576513.Subproblem 1
x + 1.277777778 = 1.552576513 Simplifying x + 1.277777778 = 1.552576513 Reorder the terms: 1.277777778 + x = 1.552576513 Solving 1.277777778 + x = 1.552576513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = 1.552576513 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = 1.552576513 + -1.277777778 x = 1.552576513 + -1.277777778 Combine like terms: 1.552576513 + -1.277777778 = 0.274798735 x = 0.274798735 Simplifying x = 0.274798735Subproblem 2
x + 1.277777778 = -1.552576513 Simplifying x + 1.277777778 = -1.552576513 Reorder the terms: 1.277777778 + x = -1.552576513 Solving 1.277777778 + x = -1.552576513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = -1.552576513 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = -1.552576513 + -1.277777778 x = -1.552576513 + -1.277777778 Combine like terms: -1.552576513 + -1.277777778 = -2.830354291 x = -2.830354291 Simplifying x = -2.830354291Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.274798735, -2.830354291}
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