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Simplifying 7x2 + -51x + -14 = 0 Reorder the terms: -14 + -51x + 7x2 = 0 Solving -14 + -51x + 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'. -2 + -7.285714286x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -7.285714286x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -7.285714286x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7.285714286x + x2 = 0 + 2 -7.285714286x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -7.285714286x + x2 = 2 The x term is -7.285714286x. Take half its coefficient (-3.642857143). Square it (13.27040816) and add it to both sides. Add '13.27040816' to each side of the equation. -7.285714286x + 13.27040816 + x2 = 2 + 13.27040816 Reorder the terms: 13.27040816 + -7.285714286x + x2 = 2 + 13.27040816 Combine like terms: 2 + 13.27040816 = 15.27040816 13.27040816 + -7.285714286x + x2 = 15.27040816 Factor a perfect square on the left side: (x + -3.642857143)(x + -3.642857143) = 15.27040816 Calculate the square root of the right side: 3.907736961 Break this problem into two subproblems by setting (x + -3.642857143) equal to 3.907736961 and -3.907736961.Subproblem 1
x + -3.642857143 = 3.907736961 Simplifying x + -3.642857143 = 3.907736961 Reorder the terms: -3.642857143 + x = 3.907736961 Solving -3.642857143 + x = 3.907736961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.642857143' to each side of the equation. -3.642857143 + 3.642857143 + x = 3.907736961 + 3.642857143 Combine like terms: -3.642857143 + 3.642857143 = 0.000000000 0.000000000 + x = 3.907736961 + 3.642857143 x = 3.907736961 + 3.642857143 Combine like terms: 3.907736961 + 3.642857143 = 7.550594104 x = 7.550594104 Simplifying x = 7.550594104Subproblem 2
x + -3.642857143 = -3.907736961 Simplifying x + -3.642857143 = -3.907736961 Reorder the terms: -3.642857143 + x = -3.907736961 Solving -3.642857143 + x = -3.907736961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.642857143' to each side of the equation. -3.642857143 + 3.642857143 + x = -3.907736961 + 3.642857143 Combine like terms: -3.642857143 + 3.642857143 = 0.000000000 0.000000000 + x = -3.907736961 + 3.642857143 x = -3.907736961 + 3.642857143 Combine like terms: -3.907736961 + 3.642857143 = -0.264879818 x = -0.264879818 Simplifying x = -0.264879818Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.550594104, -0.264879818}
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