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Simplifying (25x4 + -9x2 + -36) = 0 Reorder the terms: (-36 + -9x2 + 25x4) = 0 Remove parenthesis around (-36 + -9x2 + 25x4) -36 + -9x2 + 25x4 = 0 Solving -36 + -9x2 + 25x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.44 + -0.36x2 + x4 = 0 Move the constant term to the right: Add '1.44' to each side of the equation. -1.44 + -0.36x2 + 1.44 + x4 = 0 + 1.44 Reorder the terms: -1.44 + 1.44 + -0.36x2 + x4 = 0 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 0.00 + -0.36x2 + x4 = 0 + 1.44 -0.36x2 + x4 = 0 + 1.44 Combine like terms: 0 + 1.44 = 1.44 -0.36x2 + x4 = 1.44 The x term is -0.36x2. Take half its coefficient (-0.18). Square it (0.0324) and add it to both sides. Add '0.0324' to each side of the equation. -0.36x2 + 0.0324 + x4 = 1.44 + 0.0324 Reorder the terms: 0.0324 + -0.36x2 + x4 = 1.44 + 0.0324 Combine like terms: 1.44 + 0.0324 = 1.4724 0.0324 + -0.36x2 + x4 = 1.4724 Factor a perfect square on the left side: (x2 + -0.18)(x2 + -0.18) = 1.4724 Calculate the square root of the right side: 1.213424905 Break this problem into two subproblems by setting (x2 + -0.18) equal to 1.213424905 and -1.213424905.Subproblem 1
x2 + -0.18 = 1.213424905 Simplifying x2 + -0.18 = 1.213424905 Reorder the terms: -0.18 + x2 = 1.213424905 Solving -0.18 + x2 = 1.213424905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.18' to each side of the equation. -0.18 + 0.18 + x2 = 1.213424905 + 0.18 Combine like terms: -0.18 + 0.18 = 0.00 0.00 + x2 = 1.213424905 + 0.18 x2 = 1.213424905 + 0.18 Combine like terms: 1.213424905 + 0.18 = 1.393424905 x2 = 1.393424905 Simplifying x2 = 1.393424905 Take the square root of each side: x = {-1.180434202, 1.180434202}Subproblem 2
x2 + -0.18 = -1.213424905 Simplifying x2 + -0.18 = -1.213424905 Reorder the terms: -0.18 + x2 = -1.213424905 Solving -0.18 + x2 = -1.213424905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.18' to each side of the equation. -0.18 + 0.18 + x2 = -1.213424905 + 0.18 Combine like terms: -0.18 + 0.18 = 0.00 0.00 + x2 = -1.213424905 + 0.18 x2 = -1.213424905 + 0.18 Combine like terms: -1.213424905 + 0.18 = -1.033424905 x2 = -1.033424905 Simplifying x2 = -1.033424905 Reorder the terms: 1.033424905 + x2 = -1.033424905 + 1.033424905 Combine like terms: -1.033424905 + 1.033424905 = 0.000000000 1.033424905 + x2 = 0.000000000 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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