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Simplifying 20x3 + 3x2 + -12x = 0 Reorder the terms: -12x + 3x2 + 20x3 = 0 Solving -12x + 3x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + 3x + 20x2) = 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 '(-12 + 3x + 20x2)' equal to zero and attempt to solve: Simplifying -12 + 3x + 20x2 = 0 Solving -12 + 3x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.6 + 0.15x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.15x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.15x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.15x + x2 = 0 + 0.6 0.15x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 0.15x + x2 = 0.6 The x term is 0.15x. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15x + 0.005625 + x2 = 0.6 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = 0.6 + 0.005625 Combine like terms: 0.6 + 0.005625 = 0.605625 0.005625 + 0.15x + x2 = 0.605625 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 0.605625 Calculate the square root of the right side: 0.778219121 Break this problem into two subproblems by setting (x + 0.075) equal to 0.778219121 and -0.778219121.Subproblem 1
x + 0.075 = 0.778219121 Simplifying x + 0.075 = 0.778219121 Reorder the terms: 0.075 + x = 0.778219121 Solving 0.075 + x = 0.778219121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = 0.778219121 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 0.778219121 + -0.075 x = 0.778219121 + -0.075 Combine like terms: 0.778219121 + -0.075 = 0.703219121 x = 0.703219121 Simplifying x = 0.703219121Subproblem 2
x + 0.075 = -0.778219121 Simplifying x + 0.075 = -0.778219121 Reorder the terms: 0.075 + x = -0.778219121 Solving 0.075 + x = -0.778219121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = -0.778219121 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -0.778219121 + -0.075 x = -0.778219121 + -0.075 Combine like terms: -0.778219121 + -0.075 = -0.853219121 x = -0.853219121 Simplifying x = -0.853219121Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.703219121, -0.853219121}Solution
x = {0, 0.703219121, -0.853219121}
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