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Simplifying -2 + -2x = 8x(5 + -1x) -2 + -2x = (5 * 8x + -1x * 8x) -2 + -2x = (40x + -8x2) Solving -2 + -2x = 40x + -8x2 Solving for variable 'x'. Combine like terms: -2x + -40x = -42x -2 + -42x + 8x2 = 40x + -8x2 + -40x + 8x2 Reorder the terms: -2 + -42x + 8x2 = 40x + -40x + -8x2 + 8x2 Combine like terms: 40x + -40x = 0 -2 + -42x + 8x2 = 0 + -8x2 + 8x2 -2 + -42x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -2 + -42x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -21x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -21x + 4x2)' equal to zero and attempt to solve: Simplifying -1 + -21x + 4x2 = 0 Solving -1 + -21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -5.25x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -5.25x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -5.25x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -5.25x + x2 = 0 + 0.25 -5.25x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -5.25x + x2 = 0.25 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = 0.25 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = 0.25 + 6.890625 Combine like terms: 0.25 + 6.890625 = 7.140625 6.890625 + -5.25x + x2 = 7.140625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 7.140625 Calculate the square root of the right side: 2.672194791 Break this problem into two subproblems by setting (x + -2.625) equal to 2.672194791 and -2.672194791.Subproblem 1
x + -2.625 = 2.672194791 Simplifying x + -2.625 = 2.672194791 Reorder the terms: -2.625 + x = 2.672194791 Solving -2.625 + x = 2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 2.672194791 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 2.672194791 + 2.625 x = 2.672194791 + 2.625 Combine like terms: 2.672194791 + 2.625 = 5.297194791 x = 5.297194791 Simplifying x = 5.297194791Subproblem 2
x + -2.625 = -2.672194791 Simplifying x + -2.625 = -2.672194791 Reorder the terms: -2.625 + x = -2.672194791 Solving -2.625 + x = -2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -2.672194791 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -2.672194791 + 2.625 x = -2.672194791 + 2.625 Combine like terms: -2.672194791 + 2.625 = -0.047194791 x = -0.047194791 Simplifying x = -0.047194791Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.297194791, -0.047194791}Solution
x = {5.297194791, -0.047194791}
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