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Simplifying 9(X) = 7X2 + -9 Reorder the terms: 9X = -9 + 7X2 Solving 9X = -9 + 7X2 Solving for variable 'X'. Reorder the terms: 9 + 9X + -7X2 = -9 + 7X2 + 9 + -7X2 Reorder the terms: 9 + 9X + -7X2 = -9 + 9 + 7X2 + -7X2 Combine like terms: -9 + 9 = 0 9 + 9X + -7X2 = 0 + 7X2 + -7X2 9 + 9X + -7X2 = 7X2 + -7X2 Combine like terms: 7X2 + -7X2 = 0 9 + 9X + -7X2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.285714286 + -1.285714286X + X2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -1.285714286X + 1.285714286 + X2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -1.285714286X + X2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -1.285714286X + X2 = 0 + 1.285714286 -1.285714286X + X2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -1.285714286X + X2 = 1.285714286 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 = 1.285714286 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286X + X2 = 1.285714286 + 0.4132653063 Combine like terms: 1.285714286 + 0.4132653063 = 1.6989795923 0.4132653063 + -1.285714286X + X2 = 1.6989795923 Factor a perfect square on the left side: (X + -0.642857143)(X + -0.642857143) = 1.6989795923 Calculate the square root of the right side: 1.303449114 Break this problem into two subproblems by setting (X + -0.642857143) equal to 1.303449114 and -1.303449114.Subproblem 1
X + -0.642857143 = 1.303449114 Simplifying X + -0.642857143 = 1.303449114 Reorder the terms: -0.642857143 + X = 1.303449114 Solving -0.642857143 + X = 1.303449114 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 = 1.303449114 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + X = 1.303449114 + 0.642857143 X = 1.303449114 + 0.642857143 Combine like terms: 1.303449114 + 0.642857143 = 1.946306257 X = 1.946306257 Simplifying X = 1.946306257Subproblem 2
X + -0.642857143 = -1.303449114 Simplifying X + -0.642857143 = -1.303449114 Reorder the terms: -0.642857143 + X = -1.303449114 Solving -0.642857143 + X = -1.303449114 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 = -1.303449114 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + X = -1.303449114 + 0.642857143 X = -1.303449114 + 0.642857143 Combine like terms: -1.303449114 + 0.642857143 = -0.660591971 X = -0.660591971 Simplifying X = -0.660591971Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.946306257, -0.660591971}
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