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Simplifying (64x4) + -1(40x2) + 2 = 0 Remove parenthesis around (40x2) (64x4) + -1 * 40x2 + 2 = 0 Multiply -1 * 40 (64x4) + -40x2 + 2 = 0 Reorder the terms: 2 + -40x2 + (64x4) = 0 Solving 2 + -40x2 + (64x4) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -20x2 + (32x4)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -20x2 + (32x4))' equal to zero and attempt to solve: Simplifying 1 + -20x2 + (32x4) = 0 Solving 1 + -20x2 + (32x4) = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.03125 + -0.625x2 + x4 = 0 Move the constant term to the right: Add '-0.03125' to each side of the equation. 0.03125 + -0.625x2 + -0.03125 + x4 = 0 + -0.03125 Reorder the terms: 0.03125 + -0.03125 + -0.625x2 + x4 = 0 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + -0.625x2 + x4 = 0 + -0.03125 -0.625x2 + x4 = 0 + -0.03125 Combine like terms: 0 + -0.03125 = -0.03125 -0.625x2 + x4 = -0.03125 The x term is -0.625x2. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x2 + 0.09765625 + x4 = -0.03125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x2 + x4 = -0.03125 + 0.09765625 Combine like terms: -0.03125 + 0.09765625 = 0.06640625 0.09765625 + -0.625x2 + x4 = 0.06640625 Factor a perfect square on the left side: ((x2) + -0.3125)((x2) + -0.3125) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting ((x2) + -0.3125) equal to 0.257694102 and -0.257694102.Subproblem 1
(x2) + -0.3125 = 0.257694102 Simplifying (x2) + -0.3125 = 0.257694102 x2 + -0.3125 = 0.257694102 Reorder the terms: -0.3125 + x2 = 0.257694102 Solving -0.3125 + x2 = 0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x2 = 0.257694102 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x2 = 0.257694102 + 0.3125 x2 = 0.257694102 + 0.3125 Combine like terms: 0.257694102 + 0.3125 = 0.570194102 x2 = 0.570194102 Simplifying x2 = 0.570194102 Take the square root of each side: x = {-0.75511198, 0.75511198}Subproblem 2
(x2) + -0.3125 = -0.257694102 Simplifying (x2) + -0.3125 = -0.257694102 x2 + -0.3125 = -0.257694102 Reorder the terms: -0.3125 + x2 = -0.257694102 Solving -0.3125 + x2 = -0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x2 = -0.257694102 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x2 = -0.257694102 + 0.3125 x2 = -0.257694102 + 0.3125 Combine like terms: -0.257694102 + 0.3125 = 0.054805898 x2 = 0.054805898 Simplifying x2 = 0.054805898 Take the square root of each side: x = {-0.234106595, 0.234106595}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.75511198, 0.75511198, -0.234106595, 0.234106595}Solution
x = {-0.75511198, 0.75511198, -0.234106595, 0.234106595}
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