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Simplifying 2x2(6x2 + -5) = 9 Reorder the terms: 2x2(-5 + 6x2) = 9 (-5 * 2x2 + 6x2 * 2x2) = 9 (-10x2 + 12x4) = 9 Solving -10x2 + 12x4 = 9 Solving for variable 'x'. Reorder the terms: -9 + -10x2 + 12x4 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -10x2 + 12x4 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.75 + -0.8333333333x2 + x4 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.8333333333x2 + 0.75 + x4 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.8333333333x2 + x4 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.8333333333x2 + x4 = 0 + 0.75 -0.8333333333x2 + x4 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.8333333333x2 + x4 = 0.75 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 = 0.75 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x2 + x4 = 0.75 + 0.1736111111 Combine like terms: 0.75 + 0.1736111111 = 0.9236111111 0.1736111111 + -0.8333333333x2 + x4 = 0.9236111111 Factor a perfect square on the left side: (x2 + -0.4166666667)(x2 + -0.4166666667) = 0.9236111111 Calculate the square root of the right side: 0.961046883 Break this problem into two subproblems by setting (x2 + -0.4166666667) equal to 0.961046883 and -0.961046883.Subproblem 1
x2 + -0.4166666667 = 0.961046883 Simplifying x2 + -0.4166666667 = 0.961046883 Reorder the terms: -0.4166666667 + x2 = 0.961046883 Solving -0.4166666667 + x2 = 0.961046883 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 = 0.961046883 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x2 = 0.961046883 + 0.4166666667 x2 = 0.961046883 + 0.4166666667 Combine like terms: 0.961046883 + 0.4166666667 = 1.3777135497 x2 = 1.3777135497 Simplifying x2 = 1.3777135497 Take the square root of each side: x = {-1.173760431, 1.173760431}Subproblem 2
x2 + -0.4166666667 = -0.961046883 Simplifying x2 + -0.4166666667 = -0.961046883 Reorder the terms: -0.4166666667 + x2 = -0.961046883 Solving -0.4166666667 + x2 = -0.961046883 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 = -0.961046883 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x2 = -0.961046883 + 0.4166666667 x2 = -0.961046883 + 0.4166666667 Combine like terms: -0.961046883 + 0.4166666667 = -0.5443802163 x2 = -0.5443802163 Simplifying x2 = -0.5443802163 Reorder the terms: 0.5443802163 + x2 = -0.5443802163 + 0.5443802163 Combine like terms: -0.5443802163 + 0.5443802163 = 0.0000000000 0.5443802163 + 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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