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Simplifying 7X2 + -16X + -63 = 0 Reorder the terms: -63 + -16X + 7X2 = 0 Solving -63 + -16X + 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'. -9 + -2.285714286X + X2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -2.285714286X + 9 + X2 = 0 + 9 Reorder the terms: -9 + 9 + -2.285714286X + X2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2.285714286X + X2 = 0 + 9 -2.285714286X + X2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2.285714286X + X2 = 9 The X term is -2.285714286X. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286X + 1.306122449 + X2 = 9 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286X + X2 = 9 + 1.306122449 Combine like terms: 9 + 1.306122449 = 10.306122449 1.306122449 + -2.285714286X + X2 = 10.306122449 Factor a perfect square on the left side: (X + -1.142857143)(X + -1.142857143) = 10.306122449 Calculate the square root of the right side: 3.210315008 Break this problem into two subproblems by setting (X + -1.142857143) equal to 3.210315008 and -3.210315008.Subproblem 1
X + -1.142857143 = 3.210315008 Simplifying X + -1.142857143 = 3.210315008 Reorder the terms: -1.142857143 + X = 3.210315008 Solving -1.142857143 + X = 3.210315008 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + X = 3.210315008 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + X = 3.210315008 + 1.142857143 X = 3.210315008 + 1.142857143 Combine like terms: 3.210315008 + 1.142857143 = 4.353172151 X = 4.353172151 Simplifying X = 4.353172151Subproblem 2
X + -1.142857143 = -3.210315008 Simplifying X + -1.142857143 = -3.210315008 Reorder the terms: -1.142857143 + X = -3.210315008 Solving -1.142857143 + X = -3.210315008 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + X = -3.210315008 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + X = -3.210315008 + 1.142857143 X = -3.210315008 + 1.142857143 Combine like terms: -3.210315008 + 1.142857143 = -2.067457865 X = -2.067457865 Simplifying X = -2.067457865Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.353172151, -2.067457865}
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