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Simplifying (2.3x + -4)(x + -4) * 2 = 0 Reorder the terms: (-4 + 2.3x)(x + -4) * 2 = 0 Reorder the terms: (-4 + 2.3x)(-4 + x) * 2 = 0 Reorder the terms for easier multiplication: 2(-4 + 2.3x)(-4 + x) = 0 Multiply (-4 + 2.3x) * (-4 + x) 2(-4(-4 + x) + 2.3x * (-4 + x)) = 0 2((-4 * -4 + x * -4) + 2.3x * (-4 + x)) = 0 2((16 + -4x) + 2.3x * (-4 + x)) = 0 2(16 + -4x + (-4 * 2.3x + x * 2.3x)) = 0 2(16 + -4x + (-9.2x + 2.3x2)) = 0 Combine like terms: -4x + -9.2x = -13.2x 2(16 + -13.2x + 2.3x2) = 0 (16 * 2 + -13.2x * 2 + 2.3x2 * 2) = 0 (32 + -26.4x + 4.6x2) = 0 Solving 32 + -26.4x + 4.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.6 the coefficient of the squared term: Divide each side by '4.6'. 6.956521739 + -5.739130435x + x2 = 0 Move the constant term to the right: Add '-6.956521739' to each side of the equation. 6.956521739 + -5.739130435x + -6.956521739 + x2 = 0 + -6.956521739 Reorder the terms: 6.956521739 + -6.956521739 + -5.739130435x + x2 = 0 + -6.956521739 Combine like terms: 6.956521739 + -6.956521739 = 0.000000000 0.000000000 + -5.739130435x + x2 = 0 + -6.956521739 -5.739130435x + x2 = 0 + -6.956521739 Combine like terms: 0 + -6.956521739 = -6.956521739 -5.739130435x + x2 = -6.956521739 The x term is -5.739130435x. Take half its coefficient (-2.869565218). Square it (8.234404540) and add it to both sides. Add '8.234404540' to each side of the equation. -5.739130435x + 8.234404540 + x2 = -6.956521739 + 8.234404540 Reorder the terms: 8.234404540 + -5.739130435x + x2 = -6.956521739 + 8.234404540 Combine like terms: -6.956521739 + 8.234404540 = 1.277882801 8.234404540 + -5.739130435x + x2 = 1.277882801 Factor a perfect square on the left side: (x + -2.869565218)(x + -2.869565218) = 1.277882801 Calculate the square root of the right side: 1.130434784 Break this problem into two subproblems by setting (x + -2.869565218) equal to 1.130434784 and -1.130434784.Subproblem 1
x + -2.869565218 = 1.130434784 Simplifying x + -2.869565218 = 1.130434784 Reorder the terms: -2.869565218 + x = 1.130434784 Solving -2.869565218 + x = 1.130434784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.869565218' to each side of the equation. -2.869565218 + 2.869565218 + x = 1.130434784 + 2.869565218 Combine like terms: -2.869565218 + 2.869565218 = 0.000000000 0.000000000 + x = 1.130434784 + 2.869565218 x = 1.130434784 + 2.869565218 Combine like terms: 1.130434784 + 2.869565218 = 4.000000002 x = 4.000000002 Simplifying x = 4.000000002Subproblem 2
x + -2.869565218 = -1.130434784 Simplifying x + -2.869565218 = -1.130434784 Reorder the terms: -2.869565218 + x = -1.130434784 Solving -2.869565218 + x = -1.130434784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.869565218' to each side of the equation. -2.869565218 + 2.869565218 + x = -1.130434784 + 2.869565218 Combine like terms: -2.869565218 + 2.869565218 = 0.000000000 0.000000000 + x = -1.130434784 + 2.869565218 x = -1.130434784 + 2.869565218 Combine like terms: -1.130434784 + 2.869565218 = 1.739130434 x = 1.739130434 Simplifying x = 1.739130434Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.000000002, 1.739130434}
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