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Simplifying 2x3 + 5x = 6x5 + -20x Reorder the terms: 5x + 2x3 = 6x5 + -20x Reorder the terms: 5x + 2x3 = -20x + 6x5 Solving 5x + 2x3 = -20x + 6x5 Solving for variable 'x'. Reorder the terms: 5x + 20x + 2x3 + -6x5 = -20x + 6x5 + 20x + -6x5 Combine like terms: 5x + 20x = 25x 25x + 2x3 + -6x5 = -20x + 6x5 + 20x + -6x5 Reorder the terms: 25x + 2x3 + -6x5 = -20x + 20x + 6x5 + -6x5 Combine like terms: -20x + 20x = 0 25x + 2x3 + -6x5 = 0 + 6x5 + -6x5 25x + 2x3 + -6x5 = 6x5 + -6x5 Combine like terms: 6x5 + -6x5 = 0 25x + 2x3 + -6x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(25 + 2x2 + -6x4) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(25 + 2x2 + -6x4)' equal to zero and attempt to solve: Simplifying 25 + 2x2 + -6x4 = 0 Solving 25 + 2x2 + -6x4 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -4.166666667 + -0.3333333333x2 + x4 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + -0.3333333333x2 + 4.166666667 + x4 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + -0.3333333333x2 + x4 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + -0.3333333333x2 + x4 = 0 + 4.166666667 -0.3333333333x2 + x4 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 -0.3333333333x2 + x4 = 4.166666667 The x term is -0.3333333333x2. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x2 + 0.02777777779 + x4 = 4.166666667 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x2 + x4 = 4.166666667 + 0.02777777779 Combine like terms: 4.166666667 + 0.02777777779 = 4.19444444479 0.02777777779 + -0.3333333333x2 + x4 = 4.19444444479 Factor a perfect square on the left side: (x2 + -0.1666666667)(x2 + -0.1666666667) = 4.19444444479 Calculate the square root of the right side: 2.048034288 Break this problem into two subproblems by setting (x2 + -0.1666666667) equal to 2.048034288 and -2.048034288.Subproblem 1
x2 + -0.1666666667 = 2.048034288 Simplifying x2 + -0.1666666667 = 2.048034288 Reorder the terms: -0.1666666667 + x2 = 2.048034288 Solving -0.1666666667 + x2 = 2.048034288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x2 = 2.048034288 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x2 = 2.048034288 + 0.1666666667 x2 = 2.048034288 + 0.1666666667 Combine like terms: 2.048034288 + 0.1666666667 = 2.2147009547 x2 = 2.2147009547 Simplifying x2 = 2.2147009547 Take the square root of each side: x = {-1.488187137, 1.488187137}Subproblem 2
x2 + -0.1666666667 = -2.048034288 Simplifying x2 + -0.1666666667 = -2.048034288 Reorder the terms: -0.1666666667 + x2 = -2.048034288 Solving -0.1666666667 + x2 = -2.048034288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x2 = -2.048034288 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x2 = -2.048034288 + 0.1666666667 x2 = -2.048034288 + 0.1666666667 Combine like terms: -2.048034288 + 0.1666666667 = -1.8813676213 x2 = -1.8813676213 Simplifying x2 = -1.8813676213 Reorder the terms: 1.8813676213 + x2 = -1.8813676213 + 1.8813676213 Combine like terms: -1.8813676213 + 1.8813676213 = 0.0000000000 1.8813676213 + 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. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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