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Simplifying 12x2 + -5x + -3x2 + 5x2 + -36 = 0 Reorder the terms: -36 + -5x + 12x2 + -3x2 + 5x2 = 0 Combine like terms: 12x2 + -3x2 = 9x2 -36 + -5x + 9x2 + 5x2 = 0 Combine like terms: 9x2 + 5x2 = 14x2 -36 + -5x + 14x2 = 0 Solving -36 + -5x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -2.571428571 + -0.3571428571x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -0.3571428571x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -0.3571428571x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -0.3571428571x + x2 = 0 + 2.571428571 -0.3571428571x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -0.3571428571x + x2 = 2.571428571 The x term is -0.3571428571x. Take half its coefficient (-0.1785714286). Square it (0.03188775511) and add it to both sides. Add '0.03188775511' to each side of the equation. -0.3571428571x + 0.03188775511 + x2 = 2.571428571 + 0.03188775511 Reorder the terms: 0.03188775511 + -0.3571428571x + x2 = 2.571428571 + 0.03188775511 Combine like terms: 2.571428571 + 0.03188775511 = 2.60331632611 0.03188775511 + -0.3571428571x + x2 = 2.60331632611 Factor a perfect square on the left side: (x + -0.1785714286)(x + -0.1785714286) = 2.60331632611 Calculate the square root of the right side: 1.613479571 Break this problem into two subproblems by setting (x + -0.1785714286) equal to 1.613479571 and -1.613479571.Subproblem 1
x + -0.1785714286 = 1.613479571 Simplifying x + -0.1785714286 = 1.613479571 Reorder the terms: -0.1785714286 + x = 1.613479571 Solving -0.1785714286 + x = 1.613479571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.1785714286 + x = 1.613479571 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + x = 1.613479571 + 0.1785714286 x = 1.613479571 + 0.1785714286 Combine like terms: 1.613479571 + 0.1785714286 = 1.7920509996 x = 1.7920509996 Simplifying x = 1.7920509996Subproblem 2
x + -0.1785714286 = -1.613479571 Simplifying x + -0.1785714286 = -1.613479571 Reorder the terms: -0.1785714286 + x = -1.613479571 Solving -0.1785714286 + x = -1.613479571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.1785714286 + x = -1.613479571 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + x = -1.613479571 + 0.1785714286 x = -1.613479571 + 0.1785714286 Combine like terms: -1.613479571 + 0.1785714286 = -1.4349081424 x = -1.4349081424 Simplifying x = -1.4349081424Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7920509996, -1.4349081424}
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