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Simplifying x(7x + 9) = 6 Reorder the terms: x(9 + 7x) = 6 (9 * x + 7x * x) = 6 (9x + 7x2) = 6 Solving 9x + 7x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 9x + 7x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 9x + 7x2 = 0 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 = 0.484266703 x = 0.484266703 Simplifying x = 0.484266703Subproblem 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 = -1.769980989 x = -1.769980989 Simplifying x = -1.769980989Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.484266703, -1.769980989}
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