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Simplifying 1 = 2x(x + -2) + -1[5 + -2x(10x)] Reorder the terms: 1 = 2x(-2 + x) + -1[5 + -2x(10x)] 1 = (-2 * 2x + x * 2x) + -1[5 + -2x(10x)] 1 = (-4x + 2x2) + -1[5 + -2x(10x)] Remove parenthesis around (10x) 1 = -4x + 2x2 + -1[5 + -2x * 10x] Reorder the terms for easier multiplication: 1 = -4x + 2x2 + -1[5 + -2 * 10x * x] Multiply -2 * 10 1 = -4x + 2x2 + -1[5 + -20x * x] Multiply x * x 1 = -4x + 2x2 + -1[5 + -20x2] 1 = -4x + 2x2 + [5 * -1 + -20x2 * -1] 1 = -4x + 2x2 + [-5 + 20x2] Reorder the terms: 1 = -5 + -4x + 2x2 + 20x2 Combine like terms: 2x2 + 20x2 = 22x2 1 = -5 + -4x + 22x2 Solving 1 = -5 + -4x + 22x2 Solving for variable 'x'. Combine like terms: 1 + 5 = 6 6 + 4x + -22x2 = -5 + -4x + 22x2 + 5 + 4x + -22x2 Reorder the terms: 6 + 4x + -22x2 = -5 + 5 + -4x + 4x + 22x2 + -22x2 Combine like terms: -5 + 5 = 0 6 + 4x + -22x2 = 0 + -4x + 4x + 22x2 + -22x2 6 + 4x + -22x2 = -4x + 4x + 22x2 + -22x2 Combine like terms: -4x + 4x = 0 6 + 4x + -22x2 = 0 + 22x2 + -22x2 6 + 4x + -22x2 = 22x2 + -22x2 Combine like terms: 22x2 + -22x2 = 0 6 + 4x + -22x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 2x + -11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2x + -11x2)' equal to zero and attempt to solve: Simplifying 3 + 2x + -11x2 = 0 Solving 3 + 2x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.2727272727 + -0.1818181818x + x2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.1818181818x + 0.2727272727 + x2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.1818181818x + x2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.1818181818x + x2 = 0 + 0.2727272727 -0.1818181818x + x2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.1818181818x + x2 = 0.2727272727 The x term is -0.1818181818x. Take half its coefficient (-0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. -0.1818181818x + 0.008264462808 + x2 = 0.2727272727 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818x + x2 = 0.2727272727 + 0.008264462808 Combine like terms: 0.2727272727 + 0.008264462808 = 0.280991735508 0.008264462808 + -0.1818181818x + x2 = 0.280991735508 Factor a perfect square on the left side: (x + -0.0909090909)(x + -0.0909090909) = 0.280991735508 Calculate the square root of the right side: 0.530086536 Break this problem into two subproblems by setting (x + -0.0909090909) equal to 0.530086536 and -0.530086536.Subproblem 1
x + -0.0909090909 = 0.530086536 Simplifying x + -0.0909090909 = 0.530086536 Reorder the terms: -0.0909090909 + x = 0.530086536 Solving -0.0909090909 + x = 0.530086536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = 0.530086536 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = 0.530086536 + 0.0909090909 x = 0.530086536 + 0.0909090909 Combine like terms: 0.530086536 + 0.0909090909 = 0.6209956269 x = 0.6209956269 Simplifying x = 0.6209956269Subproblem 2
x + -0.0909090909 = -0.530086536 Simplifying x + -0.0909090909 = -0.530086536 Reorder the terms: -0.0909090909 + x = -0.530086536 Solving -0.0909090909 + x = -0.530086536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = -0.530086536 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = -0.530086536 + 0.0909090909 x = -0.530086536 + 0.0909090909 Combine like terms: -0.530086536 + 0.0909090909 = -0.4391774451 x = -0.4391774451 Simplifying x = -0.4391774451Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6209956269, -0.4391774451}Solution
x = {0.6209956269, -0.4391774451}
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