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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 = 4.127551021 2.698979592 + 3.285714286x + x2 = 4.127551021 Factor a perfect square on the left side: (x + 1.642857143)(x + 1.642857143) = 4.127551021 Calculate the square root of the right side: 2.031637522 Break this problem into two subproblems by setting (x + 1.642857143) equal to 2.031637522 and -2.031637522.Subproblem 1
x + 1.642857143 = 2.031637522 Simplifying x + 1.642857143 = 2.031637522 Reorder the terms: 1.642857143 + x = 2.031637522 Solving 1.642857143 + x = 2.031637522 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 = 2.031637522 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = 2.031637522 + -1.642857143 x = 2.031637522 + -1.642857143 Combine like terms: 2.031637522 + -1.642857143 = 0.388780379 x = 0.388780379 Simplifying x = 0.388780379Subproblem 2
x + 1.642857143 = -2.031637522 Simplifying x + 1.642857143 = -2.031637522 Reorder the terms: 1.642857143 + x = -2.031637522 Solving 1.642857143 + x = -2.031637522 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 = -2.031637522 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = -2.031637522 + -1.642857143 x = -2.031637522 + -1.642857143 Combine like terms: -2.031637522 + -1.642857143 = -3.674494665 x = -3.674494665 Simplifying x = -3.674494665Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.388780379, -3.674494665}
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