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Simplifying 14x2 + -39x + -18 = 0 Reorder the terms: -18 + -39x + 14x2 = 0 Solving -18 + -39x + 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'. -1.285714286 + -2.785714286x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -2.785714286x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -2.785714286x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -2.785714286x + x2 = 0 + 1.285714286 -2.785714286x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -2.785714286x + x2 = 1.285714286 The x term is -2.785714286x. Take half its coefficient (-1.392857143). Square it (1.940051021) and add it to both sides. Add '1.940051021' to each side of the equation. -2.785714286x + 1.940051021 + x2 = 1.285714286 + 1.940051021 Reorder the terms: 1.940051021 + -2.785714286x + x2 = 1.285714286 + 1.940051021 Combine like terms: 1.285714286 + 1.940051021 = 3.225765307 1.940051021 + -2.785714286x + x2 = 3.225765307 Factor a perfect square on the left side: (x + -1.392857143)(x + -1.392857143) = 3.225765307 Calculate the square root of the right side: 1.796041566 Break this problem into two subproblems by setting (x + -1.392857143) equal to 1.796041566 and -1.796041566.Subproblem 1
x + -1.392857143 = 1.796041566 Simplifying x + -1.392857143 = 1.796041566 Reorder the terms: -1.392857143 + x = 1.796041566 Solving -1.392857143 + x = 1.796041566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.392857143' to each side of the equation. -1.392857143 + 1.392857143 + x = 1.796041566 + 1.392857143 Combine like terms: -1.392857143 + 1.392857143 = 0.000000000 0.000000000 + x = 1.796041566 + 1.392857143 x = 1.796041566 + 1.392857143 Combine like terms: 1.796041566 + 1.392857143 = 3.188898709 x = 3.188898709 Simplifying x = 3.188898709Subproblem 2
x + -1.392857143 = -1.796041566 Simplifying x + -1.392857143 = -1.796041566 Reorder the terms: -1.392857143 + x = -1.796041566 Solving -1.392857143 + x = -1.796041566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.392857143' to each side of the equation. -1.392857143 + 1.392857143 + x = -1.796041566 + 1.392857143 Combine like terms: -1.392857143 + 1.392857143 = 0.000000000 0.000000000 + x = -1.796041566 + 1.392857143 x = -1.796041566 + 1.392857143 Combine like terms: -1.796041566 + 1.392857143 = -0.403184423 x = -0.403184423 Simplifying x = -0.403184423Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.188898709, -0.403184423}
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