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Simplifying 8x(6x + -4) = 7x + 6 Reorder the terms: 8x(-4 + 6x) = 7x + 6 (-4 * 8x + 6x * 8x) = 7x + 6 (-32x + 48x2) = 7x + 6 Reorder the terms: -32x + 48x2 = 6 + 7x Solving -32x + 48x2 = 6 + 7x Solving for variable 'x'. Reorder the terms: -6 + -32x + -7x + 48x2 = 6 + 7x + -6 + -7x Combine like terms: -32x + -7x = -39x -6 + -39x + 48x2 = 6 + 7x + -6 + -7x Reorder the terms: -6 + -39x + 48x2 = 6 + -6 + 7x + -7x Combine like terms: 6 + -6 = 0 -6 + -39x + 48x2 = 0 + 7x + -7x -6 + -39x + 48x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -6 + -39x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + -13x + 16x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -13x + 16x2)' equal to zero and attempt to solve: Simplifying -2 + -13x + 16x2 = 0 Solving -2 + -13x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.125 + -0.8125x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.8125x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.8125x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.8125x + x2 = 0 + 0.125 -0.8125x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.8125x + x2 = 0.125 The x term is -0.8125x. Take half its coefficient (-0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. -0.8125x + 0.1650390625 + x2 = 0.125 + 0.1650390625 Reorder the terms: 0.1650390625 + -0.8125x + x2 = 0.125 + 0.1650390625 Combine like terms: 0.125 + 0.1650390625 = 0.2900390625 0.1650390625 + -0.8125x + x2 = 0.2900390625 Factor a perfect square on the left side: (x + -0.40625)(x + -0.40625) = 0.2900390625 Calculate the square root of the right side: 0.538552748 Break this problem into two subproblems by setting (x + -0.40625) equal to 0.538552748 and -0.538552748.Subproblem 1
x + -0.40625 = 0.538552748 Simplifying x + -0.40625 = 0.538552748 Reorder the terms: -0.40625 + x = 0.538552748 Solving -0.40625 + x = 0.538552748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + x = 0.538552748 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + x = 0.538552748 + 0.40625 x = 0.538552748 + 0.40625 Combine like terms: 0.538552748 + 0.40625 = 0.944802748 x = 0.944802748 Simplifying x = 0.944802748Subproblem 2
x + -0.40625 = -0.538552748 Simplifying x + -0.40625 = -0.538552748 Reorder the terms: -0.40625 + x = -0.538552748 Solving -0.40625 + x = -0.538552748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + x = -0.538552748 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + x = -0.538552748 + 0.40625 x = -0.538552748 + 0.40625 Combine like terms: -0.538552748 + 0.40625 = -0.132302748 x = -0.132302748 Simplifying x = -0.132302748Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.944802748, -0.132302748}Solution
x = {0.944802748, -0.132302748}
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