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Simplifying 50x3 + 10x2 + 45x = 0 Reorder the terms: 45x + 10x2 + 50x3 = 0 Solving 45x + 10x2 + 50x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(9 + 2x + 10x2) = 0 Ignore the factor 5.Subproblem 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 '(9 + 2x + 10x2)' equal to zero and attempt to solve: Simplifying 9 + 2x + 10x2 = 0 Solving 9 + 2x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.9 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + 0.2x + -0.9 + x2 = 0.0 + -0.9 Reorder the terms: 0.9 + -0.9 + 0.2x + x2 = 0.0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + 0.2x + x2 = 0.0 + -0.9 0.2x + x2 = 0.0 + -0.9 Combine like terms: 0.0 + -0.9 = -0.9 0.2x + x2 = -0.9 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = -0.9 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = -0.9 + 0.01 Combine like terms: -0.9 + 0.01 = -0.89 0.01 + 0.2x + x2 = -0.89 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = -0.89 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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