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Simplifying 14x3 + -1x2 + -12x = 0 Reorder the terms: -12x + -1x2 + 14x3 = 0 Solving -12x + -1x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + -1x + 14x2) = 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 + -1x + 14x2)' equal to zero and attempt to solve: Simplifying -12 + -1x + 14x2 = 0 Solving -12 + -1x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.8571428571 + -0.07142857143x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -0.07142857143x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -0.07142857143x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -0.07142857143x + x2 = 0 + 0.8571428571 -0.07142857143x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -0.07142857143x + x2 = 0.8571428571 The x term is -0.07142857143x. Take half its coefficient (-0.03571428572). Square it (0.001275510204) and add it to both sides. Add '0.001275510204' to each side of the equation. -0.07142857143x + 0.001275510204 + x2 = 0.8571428571 + 0.001275510204 Reorder the terms: 0.001275510204 + -0.07142857143x + x2 = 0.8571428571 + 0.001275510204 Combine like terms: 0.8571428571 + 0.001275510204 = 0.858418367304 0.001275510204 + -0.07142857143x + x2 = 0.858418367304 Factor a perfect square on the left side: (x + -0.03571428572)(x + -0.03571428572) = 0.858418367304 Calculate the square root of the right side: 0.926508698 Break this problem into two subproblems by setting (x + -0.03571428572) equal to 0.926508698 and -0.926508698.Subproblem 1
x + -0.03571428572 = 0.926508698 Simplifying x + -0.03571428572 = 0.926508698 Reorder the terms: -0.03571428572 + x = 0.926508698 Solving -0.03571428572 + x = 0.926508698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03571428572' to each side of the equation. -0.03571428572 + 0.03571428572 + x = 0.926508698 + 0.03571428572 Combine like terms: -0.03571428572 + 0.03571428572 = 0.00000000000 0.00000000000 + x = 0.926508698 + 0.03571428572 x = 0.926508698 + 0.03571428572 Combine like terms: 0.926508698 + 0.03571428572 = 0.96222298372 x = 0.96222298372 Simplifying x = 0.96222298372Subproblem 2
x + -0.03571428572 = -0.926508698 Simplifying x + -0.03571428572 = -0.926508698 Reorder the terms: -0.03571428572 + x = -0.926508698 Solving -0.03571428572 + x = -0.926508698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03571428572' to each side of the equation. -0.03571428572 + 0.03571428572 + x = -0.926508698 + 0.03571428572 Combine like terms: -0.03571428572 + 0.03571428572 = 0.00000000000 0.00000000000 + x = -0.926508698 + 0.03571428572 x = -0.926508698 + 0.03571428572 Combine like terms: -0.926508698 + 0.03571428572 = -0.89079441228 x = -0.89079441228 Simplifying x = -0.89079441228Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.96222298372, -0.89079441228}Solution
x = {0, 0.96222298372, -0.89079441228}
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