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Simplifying 10x3 + -35x + -6x2 = 0 Reorder the terms: -35x + -6x2 + 10x3 = 0 Solving -35x + -6x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-35 + -6x + 10x2) = 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 '(-35 + -6x + 10x2)' equal to zero and attempt to solve: Simplifying -35 + -6x + 10x2 = 0 Solving -35 + -6x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3.5 + -0.6x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -0.6x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -0.6x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -0.6x + x2 = 0 + 3.5 -0.6x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -0.6x + x2 = 3.5 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 = 3.5 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 3.5 + 0.09 Combine like terms: 3.5 + 0.09 = 3.59 0.09 + -0.6x + x2 = 3.59 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 3.59 Calculate the square root of the right side: 1.894729532 Break this problem into two subproblems by setting (x + -0.3) equal to 1.894729532 and -1.894729532.Subproblem 1
x + -0.3 = 1.894729532 Simplifying x + -0.3 = 1.894729532 Reorder the terms: -0.3 + x = 1.894729532 Solving -0.3 + x = 1.894729532 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 = 1.894729532 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.894729532 + 0.3 x = 1.894729532 + 0.3 Combine like terms: 1.894729532 + 0.3 = 2.194729532 x = 2.194729532 Simplifying x = 2.194729532Subproblem 2
x + -0.3 = -1.894729532 Simplifying x + -0.3 = -1.894729532 Reorder the terms: -0.3 + x = -1.894729532 Solving -0.3 + x = -1.894729532 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 = -1.894729532 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.894729532 + 0.3 x = -1.894729532 + 0.3 Combine like terms: -1.894729532 + 0.3 = -1.594729532 x = -1.594729532 Simplifying x = -1.594729532Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.194729532, -1.594729532}Solution
x = {0, 2.194729532, -1.594729532}
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