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Simplifying 14x2 + 102x + 7 = 0 Reorder the terms: 7 + 102x + 14x2 = 0 Solving 7 + 102x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.5 + 7.285714286x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 7.285714286x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 7.285714286x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 7.285714286x + x2 = 0 + -0.5 7.285714286x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 7.285714286x + x2 = -0.5 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 = -0.5 + 13.27040816 Reorder the terms: 13.27040816 + 7.285714286x + x2 = -0.5 + 13.27040816 Combine like terms: -0.5 + 13.27040816 = 12.77040816 13.27040816 + 7.285714286x + x2 = 12.77040816 Factor a perfect square on the left side: (x + 3.642857143)(x + 3.642857143) = 12.77040816 Calculate the square root of the right side: 3.573570786 Break this problem into two subproblems by setting (x + 3.642857143) equal to 3.573570786 and -3.573570786.Subproblem 1
x + 3.642857143 = 3.573570786 Simplifying x + 3.642857143 = 3.573570786 Reorder the terms: 3.642857143 + x = 3.573570786 Solving 3.642857143 + x = 3.573570786 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 = 3.573570786 + -3.642857143 Combine like terms: 3.642857143 + -3.642857143 = 0.000000000 0.000000000 + x = 3.573570786 + -3.642857143 x = 3.573570786 + -3.642857143 Combine like terms: 3.573570786 + -3.642857143 = -0.069286357 x = -0.069286357 Simplifying x = -0.069286357Subproblem 2
x + 3.642857143 = -3.573570786 Simplifying x + 3.642857143 = -3.573570786 Reorder the terms: 3.642857143 + x = -3.573570786 Solving 3.642857143 + x = -3.573570786 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 = -3.573570786 + -3.642857143 Combine like terms: 3.642857143 + -3.642857143 = 0.000000000 0.000000000 + x = -3.573570786 + -3.642857143 x = -3.573570786 + -3.642857143 Combine like terms: -3.573570786 + -3.642857143 = -7.216427929 x = -7.216427929 Simplifying x = -7.216427929Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.069286357, -7.216427929}
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