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Simplifying [2(x + -4)][2(x + -4)] = 26 Reorder the terms: [2(-4 + x)][2(x + -4)] = 26 [(-4 * 2 + x * 2)][2(x + -4)] = 26 [(-8 + 2x)][2(x + -4)] = 26 Reorder the terms: [-8 + 2x][2(-4 + x)] = 26 [-8 + 2x][(-4 * 2 + x * 2)] = 26 [-8 + 2x][(-8 + 2x)] = 26 Multiply [-8 + 2x] * [-8 + 2x] [-8[-8 + 2x] + 2x * [-8 + 2x]] = 26 [[-8 * -8 + 2x * -8] + 2x * [-8 + 2x]] = 26 [[64 + -16x] + 2x * [-8 + 2x]] = 26 [64 + -16x + [-8 * 2x + 2x * 2x]] = 26 [64 + -16x + [-16x + 4x2]] = 26 Combine like terms: -16x + -16x = -32x [64 + -32x + 4x2] = 26 Solving 64 + -32x + 4x2 = 26 Solving for variable 'x'. Reorder the terms: 64 + -26 + -32x + 4x2 = 26 + -26 Combine like terms: 64 + -26 = 38 38 + -32x + 4x2 = 26 + -26 Combine like terms: 26 + -26 = 0 38 + -32x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(19 + -16x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + -16x + 2x2)' equal to zero and attempt to solve: Simplifying 19 + -16x + 2x2 = 0 Solving 19 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 9.5 + -8x + x2 = 0 Move the constant term to the right: Add '-9.5' to each side of the equation. 9.5 + -8x + -9.5 + x2 = 0 + -9.5 Reorder the terms: 9.5 + -9.5 + -8x + x2 = 0 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + -8x + x2 = 0 + -9.5 -8x + x2 = 0 + -9.5 Combine like terms: 0 + -9.5 = -9.5 -8x + x2 = -9.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -9.5 + 16 Reorder the terms: 16 + -8x + x2 = -9.5 + 16 Combine like terms: -9.5 + 16 = 6.5 16 + -8x + x2 = 6.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + -4) equal to 2.549509757 and -2.549509757.Subproblem 1
x + -4 = 2.549509757 Simplifying x + -4 = 2.549509757 Reorder the terms: -4 + x = 2.549509757 Solving -4 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.549509757 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.549509757 + 4 x = 2.549509757 + 4 Combine like terms: 2.549509757 + 4 = 6.549509757 x = 6.549509757 Simplifying x = 6.549509757Subproblem 2
x + -4 = -2.549509757 Simplifying x + -4 = -2.549509757 Reorder the terms: -4 + x = -2.549509757 Solving -4 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.549509757 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.549509757 + 4 x = -2.549509757 + 4 Combine like terms: -2.549509757 + 4 = 1.450490243 x = 1.450490243 Simplifying x = 1.450490243Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.549509757, 1.450490243}Solution
x = {6.549509757, 1.450490243}
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