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Simplifying 100x3 + -40x2 = 6x Reorder the terms: -40x2 + 100x3 = 6x Solving -40x2 + 100x3 = 6x Solving for variable 'x'. Reorder the terms: -6x + -40x2 + 100x3 = 6x + -6x Combine like terms: 6x + -6x = 0 -6x + -40x2 + 100x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-3 + -20x + 50x2) = 0 Ignore the factor 2.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 '(-3 + -20x + 50x2)' equal to zero and attempt to solve: Simplifying -3 + -20x + 50x2 = 0 Solving -3 + -20x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.06 + -0.4x + x2 = 0.0 Move the constant term to the right: Add '0.06' to each side of the equation. -0.06 + -0.4x + 0.06 + x2 = 0.0 + 0.06 Reorder the terms: -0.06 + 0.06 + -0.4x + x2 = 0.0 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + -0.4x + x2 = 0.0 + 0.06 -0.4x + x2 = 0.0 + 0.06 Combine like terms: 0.0 + 0.06 = 0.06 -0.4x + x2 = 0.06 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 = 0.06 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.06 + 0.04 Combine like terms: 0.06 + 0.04 = 0.1 0.04 + -0.4x + x2 = 0.1 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.1 Calculate the square root of the right side: 0.316227766 Break this problem into two subproblems by setting (x + -0.2) equal to 0.316227766 and -0.316227766.Subproblem 1
x + -0.2 = 0.316227766 Simplifying x + -0.2 = 0.316227766 Reorder the terms: -0.2 + x = 0.316227766 Solving -0.2 + x = 0.316227766 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 = 0.316227766 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.316227766 + 0.2 x = 0.316227766 + 0.2 Combine like terms: 0.316227766 + 0.2 = 0.516227766 x = 0.516227766 Simplifying x = 0.516227766Subproblem 2
x + -0.2 = -0.316227766 Simplifying x + -0.2 = -0.316227766 Reorder the terms: -0.2 + x = -0.316227766 Solving -0.2 + x = -0.316227766 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 = -0.316227766 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.316227766 + 0.2 x = -0.316227766 + 0.2 Combine like terms: -0.316227766 + 0.2 = -0.116227766 x = -0.116227766 Simplifying x = -0.116227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.516227766, -0.116227766}Solution
x = {0, 0.516227766, -0.116227766}
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