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Simplifying 7x2 + 9x + -2 = 0 Reorder the terms: -2 + 9x + 7x2 = 0 Solving -2 + 9x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 1.285714286x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 1.285714286x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 1.285714286x + x2 = 0 + 0.2857142857 1.285714286x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 1.285714286x + x2 = 0.2857142857 The x term is 1.285714286x. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286x + 0.4132653063 + x2 = 0.2857142857 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = 0.2857142857 + 0.4132653063 Combine like terms: 0.2857142857 + 0.4132653063 = 0.698979592 0.4132653063 + 1.285714286x + x2 = 0.698979592 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = 0.698979592 Calculate the square root of the right side: 0.836049994 Break this problem into two subproblems by setting (x + 0.642857143) equal to 0.836049994 and -0.836049994.Subproblem 1
x + 0.642857143 = 0.836049994 Simplifying x + 0.642857143 = 0.836049994 Reorder the terms: 0.642857143 + x = 0.836049994 Solving 0.642857143 + x = 0.836049994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = 0.836049994 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 0.836049994 + -0.642857143 x = 0.836049994 + -0.642857143 Combine like terms: 0.836049994 + -0.642857143 = 0.193192851 x = 0.193192851 Simplifying x = 0.193192851Subproblem 2
x + 0.642857143 = -0.836049994 Simplifying x + 0.642857143 = -0.836049994 Reorder the terms: 0.642857143 + x = -0.836049994 Solving 0.642857143 + x = -0.836049994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = -0.836049994 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -0.836049994 + -0.642857143 x = -0.836049994 + -0.642857143 Combine like terms: -0.836049994 + -0.642857143 = -1.478907137 x = -1.478907137 Simplifying x = -1.478907137Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.193192851, -1.478907137}
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