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Simplifying 7x2 + 23x + 10 = 0 Reorder the terms: 10 + 23x + 7x2 = 0 Solving 10 + 23x + 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'. 1.428571429 + 3.285714286x + x2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + 3.285714286x + -1.428571429 + x2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + 3.285714286x + x2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + 3.285714286x + x2 = 0 + -1.428571429 3.285714286x + x2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 3.285714286x + x2 = -1.428571429 The x term is 3.285714286x. Take half its coefficient (1.642857143). Square it (2.698979592) and add it to both sides. Add '2.698979592' to each side of the equation. 3.285714286x + 2.698979592 + x2 = -1.428571429 + 2.698979592 Reorder the terms: 2.698979592 + 3.285714286x + x2 = -1.428571429 + 2.698979592 Combine like terms: -1.428571429 + 2.698979592 = 1.270408163 2.698979592 + 3.285714286x + x2 = 1.270408163 Factor a perfect square on the left side: (x + 1.642857143)(x + 1.642857143) = 1.270408163 Calculate the square root of the right side: 1.127123845 Break this problem into two subproblems by setting (x + 1.642857143) equal to 1.127123845 and -1.127123845.Subproblem 1
x + 1.642857143 = 1.127123845 Simplifying x + 1.642857143 = 1.127123845 Reorder the terms: 1.642857143 + x = 1.127123845 Solving 1.642857143 + x = 1.127123845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x = 1.127123845 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = 1.127123845 + -1.642857143 x = 1.127123845 + -1.642857143 Combine like terms: 1.127123845 + -1.642857143 = -0.515733298 x = -0.515733298 Simplifying x = -0.515733298Subproblem 2
x + 1.642857143 = -1.127123845 Simplifying x + 1.642857143 = -1.127123845 Reorder the terms: 1.642857143 + x = -1.127123845 Solving 1.642857143 + x = -1.127123845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x = -1.127123845 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = -1.127123845 + -1.642857143 x = -1.127123845 + -1.642857143 Combine like terms: -1.127123845 + -1.642857143 = -2.769980988 x = -2.769980988 Simplifying x = -2.769980988Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.515733298, -2.769980988}
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