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Simplifying 5x4 + -2x3 + -2x2 = 0 Reorder the terms: -2x2 + -2x3 + 5x4 = 0 Solving -2x2 + -2x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-2 + -2x + 5x2) = 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 '(-2 + -2x + 5x2)' equal to zero and attempt to solve: Simplifying -2 + -2x + 5x2 = 0 Solving -2 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.4x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.4x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.4x + x2 = 0 + 0.4 -0.4x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.4x + x2 = 0.4 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 = 0.4 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.4 + 0.04 Combine like terms: 0.4 + 0.04 = 0.44 0.04 + -0.4x + x2 = 0.44 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x + -0.2) equal to 0.663324958 and -0.663324958.Subproblem 1
x + -0.2 = 0.663324958 Simplifying x + -0.2 = 0.663324958 Reorder the terms: -0.2 + x = 0.663324958 Solving -0.2 + x = 0.663324958 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 = 0.663324958 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.663324958 + 0.2 x = 0.663324958 + 0.2 Combine like terms: 0.663324958 + 0.2 = 0.863324958 x = 0.863324958 Simplifying x = 0.863324958Subproblem 2
x + -0.2 = -0.663324958 Simplifying x + -0.2 = -0.663324958 Reorder the terms: -0.2 + x = -0.663324958 Solving -0.2 + x = -0.663324958 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 = -0.663324958 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.663324958 + 0.2 x = -0.663324958 + 0.2 Combine like terms: -0.663324958 + 0.2 = -0.463324958 x = -0.463324958 Simplifying x = -0.463324958Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.863324958, -0.463324958}Solution
x = {0, 0.863324958, -0.463324958}
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