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Simplifying 16x + -20x3 + -60x2 = 0 Reorder the terms: 16x + -60x2 + -20x3 = 0 Solving 16x + -60x2 + -20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(4 + -15x + -5x2) = 0 Ignore the factor 4.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 '(4 + -15x + -5x2)' equal to zero and attempt to solve: Simplifying 4 + -15x + -5x2 = 0 Solving 4 + -15x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.8 + 3x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 3x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 3x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 3x + x2 = 0 + 0.8 3x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 3x + x2 = 0.8 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 0.8 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.8 + 2.25 Combine like terms: 0.8 + 2.25 = 3.05 2.25 + 3x + x2 = 3.05 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.05 Calculate the square root of the right side: 1.74642492 Break this problem into two subproblems by setting (x + 1.5) equal to 1.74642492 and -1.74642492.Subproblem 1
x + 1.5 = 1.74642492 Simplifying x + 1.5 = 1.74642492 Reorder the terms: 1.5 + x = 1.74642492 Solving 1.5 + x = 1.74642492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.74642492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.74642492 + -1.5 x = 1.74642492 + -1.5 Combine like terms: 1.74642492 + -1.5 = 0.24642492 x = 0.24642492 Simplifying x = 0.24642492Subproblem 2
x + 1.5 = -1.74642492 Simplifying x + 1.5 = -1.74642492 Reorder the terms: 1.5 + x = -1.74642492 Solving 1.5 + x = -1.74642492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.74642492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.74642492 + -1.5 x = -1.74642492 + -1.5 Combine like terms: -1.74642492 + -1.5 = -3.24642492 x = -3.24642492 Simplifying x = -3.24642492Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.24642492, -3.24642492}Solution
x = {0, 0.24642492, -3.24642492}
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