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Simplifying -13x3 + x2 + 84x = 0 Reorder the terms: 84x + x2 + -13x3 = 0 Solving 84x + x2 + -13x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(84 + x + -13x2) = 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 '(84 + x + -13x2)' equal to zero and attempt to solve: Simplifying 84 + x + -13x2 = 0 Solving 84 + x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -6.461538462 + -0.07692307692x + x2 = 0 Move the constant term to the right: Add '6.461538462' to each side of the equation. -6.461538462 + -0.07692307692x + 6.461538462 + x2 = 0 + 6.461538462 Reorder the terms: -6.461538462 + 6.461538462 + -0.07692307692x + x2 = 0 + 6.461538462 Combine like terms: -6.461538462 + 6.461538462 = 0.000000000 0.000000000 + -0.07692307692x + x2 = 0 + 6.461538462 -0.07692307692x + x2 = 0 + 6.461538462 Combine like terms: 0 + 6.461538462 = 6.461538462 -0.07692307692x + x2 = 6.461538462 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.07692307692x + 0.25 + x2 = 6.461538462 + 0.25 Reorder the terms: 0.25 + -0.07692307692x + x2 = 6.461538462 + 0.25 Combine like terms: 6.461538462 + 0.25 = 6.711538462 0.25 + -0.07692307692x + x2 = 6.711538462 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 6.711538462 Calculate the square root of the right side: 2.590663711 Break this problem into two subproblems by setting (x + 0.5) equal to 2.590663711 and -2.590663711.Subproblem 1
x + 0.5 = 2.590663711 Simplifying x + 0.5 = 2.590663711 Reorder the terms: 0.5 + x = 2.590663711 Solving 0.5 + x = 2.590663711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.590663711 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.590663711 + -0.5 x = 2.590663711 + -0.5 Combine like terms: 2.590663711 + -0.5 = 2.090663711 x = 2.090663711 Simplifying x = 2.090663711Subproblem 2
x + 0.5 = -2.590663711 Simplifying x + 0.5 = -2.590663711 Reorder the terms: 0.5 + x = -2.590663711 Solving 0.5 + x = -2.590663711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.590663711 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.590663711 + -0.5 x = -2.590663711 + -0.5 Combine like terms: -2.590663711 + -0.5 = -3.090663711 x = -3.090663711 Simplifying x = -3.090663711Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.090663711, -3.090663711}Solution
x = {0, 2.090663711, -3.090663711}
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