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Simplifying 4x4 + 20x3 + 8x2 = 0 Reorder the terms: 8x2 + 20x3 + 4x4 = 0 Solving 8x2 + 20x3 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(2 + 5x + x2) = 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 '(2 + 5x + x2)' equal to zero and attempt to solve: Simplifying 2 + 5x + x2 = 0 Solving 2 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x + x2 = 0 + -2 5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 5x + x2 = -2 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -2 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -2 + 6.25 Combine like terms: -2 + 6.25 = 4.25 6.25 + 5x + x2 = 4.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 2.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 2.5 = 2.061552813 Simplifying x + 2.5 = 2.061552813 Reorder the terms: 2.5 + x = 2.061552813 Solving 2.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.061552813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.061552813 + -2.5 x = 2.061552813 + -2.5 Combine like terms: 2.061552813 + -2.5 = -0.438447187 x = -0.438447187 Simplifying x = -0.438447187Subproblem 2
x + 2.5 = -2.061552813 Simplifying x + 2.5 = -2.061552813 Reorder the terms: 2.5 + x = -2.061552813 Solving 2.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.061552813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.061552813 + -2.5 x = -2.061552813 + -2.5 Combine like terms: -2.061552813 + -2.5 = -4.561552813 x = -4.561552813 Simplifying x = -4.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.438447187, -4.561552813}Solution
x = {0, -0.438447187, -4.561552813}
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