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Simplifying 2x3 + 2x2 + -84x = x Reorder the terms: -84x + 2x2 + 2x3 = x Solving -84x + 2x2 + 2x3 = x Solving for variable 'x'. Reorder the terms: -84x + -1x + 2x2 + 2x3 = x + -1x Combine like terms: -84x + -1x = -85x -85x + 2x2 + 2x3 = x + -1x Combine like terms: x + -1x = 0 -85x + 2x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-85 + 2x + 2x2) = 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 '(-85 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying -85 + 2x + 2x2 = 0 Solving -85 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -42.5 + x + x2 = 0 Move the constant term to the right: Add '42.5' to each side of the equation. -42.5 + x + 42.5 + x2 = 0 + 42.5 Reorder the terms: -42.5 + 42.5 + x + x2 = 0 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x + x2 = 0 + 42.5 x + x2 = 0 + 42.5 Combine like terms: 0 + 42.5 = 42.5 x + x2 = 42.5 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. + 0.25 + x2 = 42.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 42.5 + 0.25 Combine like terms: 42.5 + 0.25 = 42.75 1.25 + x2 = 42.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 42.75 Calculate the square root of the right side: 6.538348415 Break this problem into two subproblems by setting (x + 0.5) equal to 6.538348415 and -6.538348415.Subproblem 1
x + 0.5 = 6.538348415 Simplifying x + 0.5 = 6.538348415 Reorder the terms: 0.5 + x = 6.538348415 Solving 0.5 + x = 6.538348415 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 = 6.538348415 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.538348415 + -0.5 x = 6.538348415 + -0.5 Combine like terms: 6.538348415 + -0.5 = 6.038348415 x = 6.038348415 Simplifying x = 6.038348415Subproblem 2
x + 0.5 = -6.538348415 Simplifying x + 0.5 = -6.538348415 Reorder the terms: 0.5 + x = -6.538348415 Solving 0.5 + x = -6.538348415 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 = -6.538348415 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.538348415 + -0.5 x = -6.538348415 + -0.5 Combine like terms: -6.538348415 + -0.5 = -7.038348415 x = -7.038348415 Simplifying x = -7.038348415Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.038348415, -7.038348415}Solution
x = {0, 6.038348415, -7.038348415}
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