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Simplifying 2x4 + 3x3 + -8x2 = 0 Reorder the terms: -8x2 + 3x3 + 2x4 = 0 Solving -8x2 + 3x3 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-8 + 3x + 2x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-8 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -8 + 3x + 2x2 = 0 Solving -8 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + 1.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.5x + x2 = 0 + 4 1.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.5x + x2 = 4 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 4 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 4 + 0.5625 Combine like terms: 4 + 0.5625 = 4.5625 0.5625 + 1.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + 0.75) equal to 2.136000936 and -2.136000936.Subproblem 1
x + 0.75 = 2.136000936 Simplifying x + 0.75 = 2.136000936 Reorder the terms: 0.75 + x = 2.136000936 Solving 0.75 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.136000936 + -0.75 x = 2.136000936 + -0.75 Combine like terms: 2.136000936 + -0.75 = 1.386000936 x = 1.386000936 Simplifying x = 1.386000936Subproblem 2
x + 0.75 = -2.136000936 Simplifying x + 0.75 = -2.136000936 Reorder the terms: 0.75 + x = -2.136000936 Solving 0.75 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.136000936 + -0.75 x = -2.136000936 + -0.75 Combine like terms: -2.136000936 + -0.75 = -2.886000936 x = -2.886000936 Simplifying x = -2.886000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.386000936, -2.886000936}Solution
x = {0, 1.386000936, -2.886000936}
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