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Simplifying 12 + 3x + -35x2 = 0 Solving 12 + 3x + -35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -0.3428571429 + -0.08571428571x + x2 = 0 Move the constant term to the right: Add '0.3428571429' to each side of the equation. -0.3428571429 + -0.08571428571x + 0.3428571429 + x2 = 0 + 0.3428571429 Reorder the terms: -0.3428571429 + 0.3428571429 + -0.08571428571x + x2 = 0 + 0.3428571429 Combine like terms: -0.3428571429 + 0.3428571429 = 0.0000000000 0.0000000000 + -0.08571428571x + x2 = 0 + 0.3428571429 -0.08571428571x + x2 = 0 + 0.3428571429 Combine like terms: 0 + 0.3428571429 = 0.3428571429 -0.08571428571x + x2 = 0.3428571429 The x term is -0.08571428571x. Take half its coefficient (-0.04285714286). Square it (0.001836734694) and add it to both sides. Add '0.001836734694' to each side of the equation. -0.08571428571x + 0.001836734694 + x2 = 0.3428571429 + 0.001836734694 Reorder the terms: 0.001836734694 + -0.08571428571x + x2 = 0.3428571429 + 0.001836734694 Combine like terms: 0.3428571429 + 0.001836734694 = 0.344693877594 0.001836734694 + -0.08571428571x + x2 = 0.344693877594 Factor a perfect square on the left side: (x + -0.04285714286)(x + -0.04285714286) = 0.344693877594 Calculate the square root of the right side: 0.58710636 Break this problem into two subproblems by setting (x + -0.04285714286) equal to 0.58710636 and -0.58710636.Subproblem 1
x + -0.04285714286 = 0.58710636 Simplifying x + -0.04285714286 = 0.58710636 Reorder the terms: -0.04285714286 + x = 0.58710636 Solving -0.04285714286 + x = 0.58710636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04285714286' to each side of the equation. -0.04285714286 + 0.04285714286 + x = 0.58710636 + 0.04285714286 Combine like terms: -0.04285714286 + 0.04285714286 = 0.00000000000 0.00000000000 + x = 0.58710636 + 0.04285714286 x = 0.58710636 + 0.04285714286 Combine like terms: 0.58710636 + 0.04285714286 = 0.62996350286 x = 0.62996350286 Simplifying x = 0.62996350286Subproblem 2
x + -0.04285714286 = -0.58710636 Simplifying x + -0.04285714286 = -0.58710636 Reorder the terms: -0.04285714286 + x = -0.58710636 Solving -0.04285714286 + x = -0.58710636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04285714286' to each side of the equation. -0.04285714286 + 0.04285714286 + x = -0.58710636 + 0.04285714286 Combine like terms: -0.04285714286 + 0.04285714286 = 0.00000000000 0.00000000000 + x = -0.58710636 + 0.04285714286 x = -0.58710636 + 0.04285714286 Combine like terms: -0.58710636 + 0.04285714286 = -0.54424921714 x = -0.54424921714 Simplifying x = -0.54424921714Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.62996350286, -0.54424921714}
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