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Simplifying 12x2 + 8x = 1000000 Reorder the terms: 8x + 12x2 = 1000000 Solving 8x + 12x2 = 1000000 Solving for variable 'x'. Reorder the terms: -1000000 + 8x + 12x2 = 1000000 + -1000000 Combine like terms: 1000000 + -1000000 = 0 -1000000 + 8x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-250000 + 2x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-250000 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying -250000 + 2x + 3x2 = 0 Solving -250000 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -83333.33333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '83333.33333' to each side of the equation. -83333.33333 + 0.6666666667x + 83333.33333 + x2 = 0 + 83333.33333 Reorder the terms: -83333.33333 + 83333.33333 + 0.6666666667x + x2 = 0 + 83333.33333 Combine like terms: -83333.33333 + 83333.33333 = 0.00000 0.00000 + 0.6666666667x + x2 = 0 + 83333.33333 0.6666666667x + x2 = 0 + 83333.33333 Combine like terms: 0 + 83333.33333 = 83333.33333 0.6666666667x + x2 = 83333.33333 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 83333.33333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 83333.33333 + 0.1111111112 Combine like terms: 83333.33333 + 0.1111111112 = 83333.4444411112 0.1111111112 + 0.6666666667x + x2 = 83333.4444411112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 83333.4444411112 Calculate the square root of the right side: 288.675327039 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 288.675327039 and -288.675327039.Subproblem 1
x + 0.3333333334 = 288.675327039 Simplifying x + 0.3333333334 = 288.675327039 Reorder the terms: 0.3333333334 + x = 288.675327039 Solving 0.3333333334 + x = 288.675327039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 288.675327039 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 288.675327039 + -0.3333333334 x = 288.675327039 + -0.3333333334 Combine like terms: 288.675327039 + -0.3333333334 = 288.3419937056 x = 288.3419937056 Simplifying x = 288.3419937056Subproblem 2
x + 0.3333333334 = -288.675327039 Simplifying x + 0.3333333334 = -288.675327039 Reorder the terms: 0.3333333334 + x = -288.675327039 Solving 0.3333333334 + x = -288.675327039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -288.675327039 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -288.675327039 + -0.3333333334 x = -288.675327039 + -0.3333333334 Combine like terms: -288.675327039 + -0.3333333334 = -289.0086603724 x = -289.0086603724 Simplifying x = -289.0086603724Solution
The solution to the problem is based on the solutions from the subproblems. x = {288.3419937056, -289.0086603724}Solution
x = {288.3419937056, -289.0086603724}
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