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Simplifying (2x4) + (4x3) + 10x2 = 0 Reorder the terms: 10x2 + (4x3) + (2x4) = 0 Solving 10x2 + (4x3) + (2x4) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(5 + (2x) + x2) = 0 Ignore the factor 2.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 '(5 + (2x) + x2)' equal to zero and attempt to solve: Simplifying 5 + (2x) + x2 = 0 Solving 5 + (2x) + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + (2x) + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + (2x) + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + (2x) + x2 = 0 + -5 (2x) + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 (2x) + x2 = -5 The x term is (2x). Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. (2x) + 1 + x2 = -5 + 1 Reorder the terms: 1 + (2x) + x2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + (2x) + x2 = -4 Factor a perfect square on the left side: (x + 1)(x + 1) = -4 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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