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Simplifying 34x * 34x * 34x + 2x * 2x + -21x = 0 Reorder the terms for easier multiplication: 34 * 34 * 34x * x * x + 2x * 2x + -21x = 0 Multiply 34 * 34 1156 * 34x * x * x + 2x * 2x + -21x = 0 Multiply 1156 * 34 39304x * x * x + 2x * 2x + -21x = 0 Multiply x * x 39304x2 * x + 2x * 2x + -21x = 0 Multiply x2 * x 39304x3 + 2x * 2x + -21x = 0 Reorder the terms for easier multiplication: 39304x3 + 2 * 2x * x + -21x = 0 Multiply 2 * 2 39304x3 + 4x * x + -21x = 0 Multiply x * x 39304x3 + 4x2 + -21x = 0 Reorder the terms: -21x + 4x2 + 39304x3 = 0 Solving -21x + 4x2 + 39304x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-21 + 4x + 39304x2) = 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 '(-21 + 4x + 39304x2)' equal to zero and attempt to solve: Simplifying -21 + 4x + 39304x2 = 0 Solving -21 + 4x + 39304x2 = 0 Begin completing the square. Divide all terms by 39304 the coefficient of the squared term: Divide each side by '39304'. -0.0005342967637 + 0.0001017708121x + x2 = 0 Move the constant term to the right: Add '0.0005342967637' to each side of the equation. -0.0005342967637 + 0.0001017708121x + 0.0005342967637 + x2 = 0 + 0.0005342967637 Reorder the terms: -0.0005342967637 + 0.0005342967637 + 0.0001017708121x + x2 = 0 + 0.0005342967637 Combine like terms: -0.0005342967637 + 0.0005342967637 = 0.0000000000000 0.0000000000000 + 0.0001017708121x + x2 = 0 + 0.0005342967637 0.0001017708121x + x2 = 0 + 0.0005342967637 Combine like terms: 0 + 0.0005342967637 = 0.0005342967637 0.0001017708121x + x2 = 0.0005342967637 The x term is 0.0001017708121x. Take half its coefficient (0.00005088540605). Square it (0.000000002589324549) and add it to both sides. Add '0.000000002589324549' to each side of the equation. 0.0001017708121x + 0.000000002589324549 + x2 = 0.0005342967637 + 0.000000002589324549 Reorder the terms: 0.000000002589324549 + 0.0001017708121x + x2 = 0.0005342967637 + 0.000000002589324549 Combine like terms: 0.0005342967637 + 0.000000002589324549 = 0.000534299353024549 0.000000002589324549 + 0.0001017708121x + x2 = 0.000534299353024549 Factor a perfect square on the left side: (x + 0.00005088540605)(x + 0.00005088540605) = 0.000534299353024549 Calculate the square root of the right side: 0.023114916 Break this problem into two subproblems by setting (x + 0.00005088540605) equal to 0.023114916 and -0.023114916.Subproblem 1
x + 0.00005088540605 = 0.023114916 Simplifying x + 0.00005088540605 = 0.023114916 Reorder the terms: 0.00005088540605 + x = 0.023114916 Solving 0.00005088540605 + x = 0.023114916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00005088540605' to each side of the equation. 0.00005088540605 + -0.00005088540605 + x = 0.023114916 + -0.00005088540605 Combine like terms: 0.00005088540605 + -0.00005088540605 = 0.00000000000000 0.00000000000000 + x = 0.023114916 + -0.00005088540605 x = 0.023114916 + -0.00005088540605 Combine like terms: 0.023114916 + -0.00005088540605 = 0.02306403059395 x = 0.02306403059395 Simplifying x = 0.02306403059395Subproblem 2
x + 0.00005088540605 = -0.023114916 Simplifying x + 0.00005088540605 = -0.023114916 Reorder the terms: 0.00005088540605 + x = -0.023114916 Solving 0.00005088540605 + x = -0.023114916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00005088540605' to each side of the equation. 0.00005088540605 + -0.00005088540605 + x = -0.023114916 + -0.00005088540605 Combine like terms: 0.00005088540605 + -0.00005088540605 = 0.00000000000000 0.00000000000000 + x = -0.023114916 + -0.00005088540605 x = -0.023114916 + -0.00005088540605 Combine like terms: -0.023114916 + -0.00005088540605 = -0.02316580140605 x = -0.02316580140605 Simplifying x = -0.02316580140605Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.02306403059395, -0.02316580140605}Solution
x = {0, 0.02306403059395, -0.02316580140605}
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