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Simplifying 20x4 + -8x3 + -16x2 = 0 Reorder the terms: -16x2 + -8x3 + 20x4 = 0 Solving -16x2 + -8x3 + 20x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(-4 + -2x + 5x2) = 0 Ignore the factor 4.Subproblem 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 '(-4 + -2x + 5x2)' equal to zero and attempt to solve: Simplifying -4 + -2x + 5x2 = 0 Solving -4 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.4x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.4x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.4x + x2 = 0 + 0.8 -0.4x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.4x + x2 = 0.8 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.8 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.8 + 0.04 Combine like terms: 0.8 + 0.04 = 0.84 0.04 + -0.4x + x2 = 0.84 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (x + -0.2) equal to 0.916515139 and -0.916515139.Subproblem 1
x + -0.2 = 0.916515139 Simplifying x + -0.2 = 0.916515139 Reorder the terms: -0.2 + x = 0.916515139 Solving -0.2 + x = 0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.916515139 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.916515139 + 0.2 x = 0.916515139 + 0.2 Combine like terms: 0.916515139 + 0.2 = 1.116515139 x = 1.116515139 Simplifying x = 1.116515139Subproblem 2
x + -0.2 = -0.916515139 Simplifying x + -0.2 = -0.916515139 Reorder the terms: -0.2 + x = -0.916515139 Solving -0.2 + x = -0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.916515139 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.916515139 + 0.2 x = -0.916515139 + 0.2 Combine like terms: -0.916515139 + 0.2 = -0.716515139 x = -0.716515139 Simplifying x = -0.716515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.116515139, -0.716515139}Solution
x = {0, 1.116515139, -0.716515139}
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