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Simplifying 100x3 + -60x2 + -8x = 0 Reorder the terms: -8x + -60x2 + 100x3 = 0 Solving -8x + -60x2 + 100x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-2 + -15x + 25x2) = 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 '(-2 + -15x + 25x2)' equal to zero and attempt to solve: Simplifying -2 + -15x + 25x2 = 0 Solving -2 + -15x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.08 + -0.6x + x2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + -0.6x + 0.08 + x2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + -0.6x + x2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + -0.6x + x2 = 0 + 0.08 -0.6x + x2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 -0.6x + x2 = 0.08 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 0.08 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.08 + 0.09 Combine like terms: 0.08 + 0.09 = 0.17 0.09 + -0.6x + x2 = 0.17 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.17 Calculate the square root of the right side: 0.412310563 Break this problem into two subproblems by setting (x + -0.3) equal to 0.412310563 and -0.412310563.Subproblem 1
x + -0.3 = 0.412310563 Simplifying x + -0.3 = 0.412310563 Reorder the terms: -0.3 + x = 0.412310563 Solving -0.3 + x = 0.412310563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.412310563 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.412310563 + 0.3 x = 0.412310563 + 0.3 Combine like terms: 0.412310563 + 0.3 = 0.712310563 x = 0.712310563 Simplifying x = 0.712310563Subproblem 2
x + -0.3 = -0.412310563 Simplifying x + -0.3 = -0.412310563 Reorder the terms: -0.3 + x = -0.412310563 Solving -0.3 + x = -0.412310563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.412310563 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.412310563 + 0.3 x = -0.412310563 + 0.3 Combine like terms: -0.412310563 + 0.3 = -0.112310563 x = -0.112310563 Simplifying x = -0.112310563Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.712310563, -0.112310563}Solution
x = {0, 0.712310563, -0.112310563}
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