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Simplifying 6x2 + -1x + -12 = 5 Reorder the terms: -12 + -1x + 6x2 = 5 Solving -12 + -1x + 6x2 = 5 Solving for variable 'x'. Reorder the terms: -12 + -5 + -1x + 6x2 = 5 + -5 Combine like terms: -12 + -5 = -17 -17 + -1x + 6x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -17 + -1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.833333333 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '2.833333333' to each side of the equation. -2.833333333 + -0.1666666667x + 2.833333333 + x2 = 0 + 2.833333333 Reorder the terms: -2.833333333 + 2.833333333 + -0.1666666667x + x2 = 0 + 2.833333333 Combine like terms: -2.833333333 + 2.833333333 = 0.000000000 0.000000000 + -0.1666666667x + x2 = 0 + 2.833333333 -0.1666666667x + x2 = 0 + 2.833333333 Combine like terms: 0 + 2.833333333 = 2.833333333 -0.1666666667x + x2 = 2.833333333 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 2.833333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 2.833333333 + 0.006944444447 Combine like terms: 2.833333333 + 0.006944444447 = 2.840277777447 0.006944444447 + -0.1666666667x + x2 = 2.840277777447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 2.840277777447 Calculate the square root of the right side: 1.685312368 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 1.685312368 and -1.685312368.Subproblem 1
x + -0.08333333335 = 1.685312368 Simplifying x + -0.08333333335 = 1.685312368 Reorder the terms: -0.08333333335 + x = 1.685312368 Solving -0.08333333335 + x = 1.685312368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 1.685312368 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 1.685312368 + 0.08333333335 x = 1.685312368 + 0.08333333335 Combine like terms: 1.685312368 + 0.08333333335 = 1.76864570135 x = 1.76864570135 Simplifying x = 1.76864570135Subproblem 2
x + -0.08333333335 = -1.685312368 Simplifying x + -0.08333333335 = -1.685312368 Reorder the terms: -0.08333333335 + x = -1.685312368 Solving -0.08333333335 + x = -1.685312368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -1.685312368 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -1.685312368 + 0.08333333335 x = -1.685312368 + 0.08333333335 Combine like terms: -1.685312368 + 0.08333333335 = -1.60197903465 x = -1.60197903465 Simplifying x = -1.60197903465Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.76864570135, -1.60197903465}
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