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Simplifying 5x3 + -2x2 + -5x = 0 Reorder the terms: -5x + -2x2 + 5x3 = 0 Solving -5x + -2x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + -2x + 5x2) = 0Subproblem 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 '(-5 + -2x + 5x2)' equal to zero and attempt to solve: Simplifying -5 + -2x + 5x2 = 0 Solving -5 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -0.4x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.4x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.4x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.4x + x2 = 0 + 1 -0.4x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.4x + x2 = 1 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 = 1 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 1 + 0.04 Combine like terms: 1 + 0.04 = 1.04 0.04 + -0.4x + x2 = 1.04 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (x + -0.2) equal to 1.019803903 and -1.019803903.Subproblem 1
x + -0.2 = 1.019803903 Simplifying x + -0.2 = 1.019803903 Reorder the terms: -0.2 + x = 1.019803903 Solving -0.2 + x = 1.019803903 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 = 1.019803903 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.019803903 + 0.2 x = 1.019803903 + 0.2 Combine like terms: 1.019803903 + 0.2 = 1.219803903 x = 1.219803903 Simplifying x = 1.219803903Subproblem 2
x + -0.2 = -1.019803903 Simplifying x + -0.2 = -1.019803903 Reorder the terms: -0.2 + x = -1.019803903 Solving -0.2 + x = -1.019803903 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 = -1.019803903 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.019803903 + 0.2 x = -1.019803903 + 0.2 Combine like terms: -1.019803903 + 0.2 = -0.819803903 x = -0.819803903 Simplifying x = -0.819803903Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.219803903, -0.819803903}Solution
x = {0, 1.219803903, -0.819803903}
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