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Simplifying 8x(2x + -10) = 6(x + 2) Reorder the terms: 8x(-10 + 2x) = 6(x + 2) (-10 * 8x + 2x * 8x) = 6(x + 2) (-80x + 16x2) = 6(x + 2) Reorder the terms: -80x + 16x2 = 6(2 + x) -80x + 16x2 = (2 * 6 + x * 6) -80x + 16x2 = (12 + 6x) Solving -80x + 16x2 = 12 + 6x Solving for variable 'x'. Reorder the terms: -12 + -80x + -6x + 16x2 = 12 + 6x + -12 + -6x Combine like terms: -80x + -6x = -86x -12 + -86x + 16x2 = 12 + 6x + -12 + -6x Reorder the terms: -12 + -86x + 16x2 = 12 + -12 + 6x + -6x Combine like terms: 12 + -12 = 0 -12 + -86x + 16x2 = 0 + 6x + -6x -12 + -86x + 16x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -12 + -86x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -43x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -43x + 8x2)' equal to zero and attempt to solve: Simplifying -6 + -43x + 8x2 = 0 Solving -6 + -43x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + -5.375x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -5.375x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -5.375x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -5.375x + x2 = 0 + 0.75 -5.375x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -5.375x + x2 = 0.75 The x term is -5.375x. Take half its coefficient (-2.6875). Square it (7.22265625) and add it to both sides. Add '7.22265625' to each side of the equation. -5.375x + 7.22265625 + x2 = 0.75 + 7.22265625 Reorder the terms: 7.22265625 + -5.375x + x2 = 0.75 + 7.22265625 Combine like terms: 0.75 + 7.22265625 = 7.97265625 7.22265625 + -5.375x + x2 = 7.97265625 Factor a perfect square on the left side: (x + -2.6875)(x + -2.6875) = 7.97265625 Calculate the square root of the right side: 2.82358925 Break this problem into two subproblems by setting (x + -2.6875) equal to 2.82358925 and -2.82358925.Subproblem 1
x + -2.6875 = 2.82358925 Simplifying x + -2.6875 = 2.82358925 Reorder the terms: -2.6875 + x = 2.82358925 Solving -2.6875 + x = 2.82358925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6875' to each side of the equation. -2.6875 + 2.6875 + x = 2.82358925 + 2.6875 Combine like terms: -2.6875 + 2.6875 = 0.0000 0.0000 + x = 2.82358925 + 2.6875 x = 2.82358925 + 2.6875 Combine like terms: 2.82358925 + 2.6875 = 5.51108925 x = 5.51108925 Simplifying x = 5.51108925Subproblem 2
x + -2.6875 = -2.82358925 Simplifying x + -2.6875 = -2.82358925 Reorder the terms: -2.6875 + x = -2.82358925 Solving -2.6875 + x = -2.82358925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6875' to each side of the equation. -2.6875 + 2.6875 + x = -2.82358925 + 2.6875 Combine like terms: -2.6875 + 2.6875 = 0.0000 0.0000 + x = -2.82358925 + 2.6875 x = -2.82358925 + 2.6875 Combine like terms: -2.82358925 + 2.6875 = -0.13608925 x = -0.13608925 Simplifying x = -0.13608925Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.51108925, -0.13608925}Solution
x = {5.51108925, -0.13608925}
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