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Simplifying (36x4 + -30x2 + 3) = 8 Reorder the terms: (3 + -30x2 + 36x4) = 8 Remove parenthesis around (3 + -30x2 + 36x4) 3 + -30x2 + 36x4 = 8 Solving 3 + -30x2 + 36x4 = 8 Solving for variable 'x'. Reorder the terms: 3 + -8 + -30x2 + 36x4 = 8 + -8 Combine like terms: 3 + -8 = -5 -5 + -30x2 + 36x4 = 8 + -8 Combine like terms: 8 + -8 = 0 -5 + -30x2 + 36x4 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.1388888889 + -0.8333333333x2 + x4 = 0 Move the constant term to the right: Add '0.1388888889' to each side of the equation. -0.1388888889 + -0.8333333333x2 + 0.1388888889 + x4 = 0 + 0.1388888889 Reorder the terms: -0.1388888889 + 0.1388888889 + -0.8333333333x2 + x4 = 0 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + -0.8333333333x2 + x4 = 0 + 0.1388888889 -0.8333333333x2 + x4 = 0 + 0.1388888889 Combine like terms: 0 + 0.1388888889 = 0.1388888889 -0.8333333333x2 + x4 = 0.1388888889 The x term is -0.8333333333x2. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x2 + 0.1736111111 + x4 = 0.1388888889 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x2 + x4 = 0.1388888889 + 0.1736111111 Combine like terms: 0.1388888889 + 0.1736111111 = 0.3125 0.1736111111 + -0.8333333333x2 + x4 = 0.3125 Factor a perfect square on the left side: (x2 + -0.4166666667)(x2 + -0.4166666667) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (x2 + -0.4166666667) equal to 0.559016994 and -0.559016994.Subproblem 1
x2 + -0.4166666667 = 0.559016994 Simplifying x2 + -0.4166666667 = 0.559016994 Reorder the terms: -0.4166666667 + x2 = 0.559016994 Solving -0.4166666667 + x2 = 0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x2 = 0.559016994 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x2 = 0.559016994 + 0.4166666667 x2 = 0.559016994 + 0.4166666667 Combine like terms: 0.559016994 + 0.4166666667 = 0.9756836607 x2 = 0.9756836607 Simplifying x2 = 0.9756836607 Take the square root of each side: x = {-0.987767007, 0.987767007}Subproblem 2
x2 + -0.4166666667 = -0.559016994 Simplifying x2 + -0.4166666667 = -0.559016994 Reorder the terms: -0.4166666667 + x2 = -0.559016994 Solving -0.4166666667 + x2 = -0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x2 = -0.559016994 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x2 = -0.559016994 + 0.4166666667 x2 = -0.559016994 + 0.4166666667 Combine like terms: -0.559016994 + 0.4166666667 = -0.1423503273 x2 = -0.1423503273 Simplifying x2 = -0.1423503273 Reorder the terms: 0.1423503273 + x2 = -0.1423503273 + 0.1423503273 Combine like terms: -0.1423503273 + 0.1423503273 = 0.0000000000 0.1423503273 + x2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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