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Simplifying 7x2 + -9x + -6 = 0 Reorder the terms: -6 + -9x + 7x2 = 0 Solving -6 + -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'. -0.8571428571 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -1.285714286x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -1.285714286x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -1.285714286x + x2 = 0 + 0.8571428571 -1.285714286x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -1.285714286x + x2 = 0.8571428571 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 = 0.8571428571 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 0.8571428571 + 0.4132653063 Combine like terms: 0.8571428571 + 0.4132653063 = 1.2704081634 0.4132653063 + -1.285714286x + x2 = 1.2704081634 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 1.2704081634 Calculate the square root of the right side: 1.127123846 Break this problem into two subproblems by setting (x + -0.642857143) equal to 1.127123846 and -1.127123846.Subproblem 1
x + -0.642857143 = 1.127123846 Simplifying x + -0.642857143 = 1.127123846 Reorder the terms: -0.642857143 + x = 1.127123846 Solving -0.642857143 + x = 1.127123846 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 = 1.127123846 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 1.127123846 + 0.642857143 x = 1.127123846 + 0.642857143 Combine like terms: 1.127123846 + 0.642857143 = 1.769980989 x = 1.769980989 Simplifying x = 1.769980989Subproblem 2
x + -0.642857143 = -1.127123846 Simplifying x + -0.642857143 = -1.127123846 Reorder the terms: -0.642857143 + x = -1.127123846 Solving -0.642857143 + x = -1.127123846 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 = -1.127123846 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -1.127123846 + 0.642857143 x = -1.127123846 + 0.642857143 Combine like terms: -1.127123846 + 0.642857143 = -0.484266703 x = -0.484266703 Simplifying x = -0.484266703Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.769980989, -0.484266703}
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