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Simplifying 0 = 3x7 + -84x5 + -448x3 Reorder the terms: 0 = -448x3 + -84x5 + 3x7 Solving 0 = -448x3 + -84x5 + 3x7 Solving for variable 'x'. Remove the zero: 448x3 + 84x5 + -3x7 = -448x3 + -84x5 + 3x7 + 448x3 + 84x5 + -3x7 Reorder the terms: 448x3 + 84x5 + -3x7 = -448x3 + 448x3 + -84x5 + 84x5 + 3x7 + -3x7 Combine like terms: -448x3 + 448x3 = 0 448x3 + 84x5 + -3x7 = 0 + -84x5 + 84x5 + 3x7 + -3x7 448x3 + 84x5 + -3x7 = -84x5 + 84x5 + 3x7 + -3x7 Combine like terms: -84x5 + 84x5 = 0 448x3 + 84x5 + -3x7 = 0 + 3x7 + -3x7 448x3 + 84x5 + -3x7 = 3x7 + -3x7 Combine like terms: 3x7 + -3x7 = 0 448x3 + 84x5 + -3x7 = 0 Factor out the Greatest Common Factor (GCF), 'x3'. x3(448 + 84x2 + -3x4) = 0Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(448 + 84x2 + -3x4)' equal to zero and attempt to solve: Simplifying 448 + 84x2 + -3x4 = 0 Solving 448 + 84x2 + -3x4 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -149.3333333 + -28x2 + x4 = 0 Move the constant term to the right: Add '149.3333333' to each side of the equation. -149.3333333 + -28x2 + 149.3333333 + x4 = 0 + 149.3333333 Reorder the terms: -149.3333333 + 149.3333333 + -28x2 + x4 = 0 + 149.3333333 Combine like terms: -149.3333333 + 149.3333333 = 0.0000000 0.0000000 + -28x2 + x4 = 0 + 149.3333333 -28x2 + x4 = 0 + 149.3333333 Combine like terms: 0 + 149.3333333 = 149.3333333 -28x2 + x4 = 149.3333333 The x term is -28x2. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x2 + 196 + x4 = 149.3333333 + 196 Reorder the terms: 196 + -28x2 + x4 = 149.3333333 + 196 Combine like terms: 149.3333333 + 196 = 345.3333333 196 + -28x2 + x4 = 345.3333333 Factor a perfect square on the left side: (x2 + -14)(x2 + -14) = 345.3333333 Calculate the square root of the right side: 18.583146485 Break this problem into two subproblems by setting (x2 + -14) equal to 18.583146485 and -18.583146485.Subproblem 1
x2 + -14 = 18.583146485 Simplifying x2 + -14 = 18.583146485 Reorder the terms: -14 + x2 = 18.583146485 Solving -14 + x2 = 18.583146485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x2 = 18.583146485 + 14 Combine like terms: -14 + 14 = 0 0 + x2 = 18.583146485 + 14 x2 = 18.583146485 + 14 Combine like terms: 18.583146485 + 14 = 32.583146485 x2 = 32.583146485 Simplifying x2 = 32.583146485 Take the square root of each side: x = {-5.708164896, 5.708164896}Subproblem 2
x2 + -14 = -18.583146485 Simplifying x2 + -14 = -18.583146485 Reorder the terms: -14 + x2 = -18.583146485 Solving -14 + x2 = -18.583146485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x2 = -18.583146485 + 14 Combine like terms: -14 + 14 = 0 0 + x2 = -18.583146485 + 14 x2 = -18.583146485 + 14 Combine like terms: -18.583146485 + 14 = -4.583146485 x2 = -4.583146485 Simplifying x2 = -4.583146485 Reorder the terms: 4.583146485 + x2 = -4.583146485 + 4.583146485 Combine like terms: -4.583146485 + 4.583146485 = 0.000000000 4.583146485 + 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. 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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