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Simplifying 8x3 + 4x2 + -30x = 0 Reorder the terms: -30x + 4x2 + 8x3 = 0 Solving -30x + 4x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-15 + 2x + 4x2) = 0 Ignore the factor 2.Subproblem 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 '(-15 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying -15 + 2x + 4x2 = 0 Solving -15 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 0.5x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 0.5x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 0.5x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 0.5x + x2 = 0 + 3.75 0.5x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 0.5x + x2 = 3.75 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 3.75 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 3.75 + 0.0625 Combine like terms: 3.75 + 0.0625 = 3.8125 0.0625 + 0.5x + x2 = 3.8125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (x + 0.25) equal to 1.952562419 and -1.952562419.Subproblem 1
x + 0.25 = 1.952562419 Simplifying x + 0.25 = 1.952562419 Reorder the terms: 0.25 + x = 1.952562419 Solving 0.25 + x = 1.952562419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.952562419 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.952562419 + -0.25 x = 1.952562419 + -0.25 Combine like terms: 1.952562419 + -0.25 = 1.702562419 x = 1.702562419 Simplifying x = 1.702562419Subproblem 2
x + 0.25 = -1.952562419 Simplifying x + 0.25 = -1.952562419 Reorder the terms: 0.25 + x = -1.952562419 Solving 0.25 + x = -1.952562419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.952562419 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.952562419 + -0.25 x = -1.952562419 + -0.25 Combine like terms: -1.952562419 + -0.25 = -2.202562419 x = -2.202562419 Simplifying x = -2.202562419Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.702562419, -2.202562419}Solution
x = {0, 1.702562419, -2.202562419}
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