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Simplifying 7x2 + 23x + -6 = 0 Reorder the terms: -6 + 23x + 7x2 = 0 Solving -6 + 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'. -0.8571428571 + 3.285714286x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 3.285714286x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 3.285714286x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 3.285714286x + x2 = 0 + 0.8571428571 3.285714286x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 3.285714286x + x2 = 0.8571428571 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 = 0.8571428571 + 2.698979592 Reorder the terms: 2.698979592 + 3.285714286x + x2 = 0.8571428571 + 2.698979592 Combine like terms: 0.8571428571 + 2.698979592 = 3.5561224491 2.698979592 + 3.285714286x + x2 = 3.5561224491 Factor a perfect square on the left side: (x + 1.642857143)(x + 1.642857143) = 3.5561224491 Calculate the square root of the right side: 1.885768398 Break this problem into two subproblems by setting (x + 1.642857143) equal to 1.885768398 and -1.885768398.Subproblem 1
x + 1.642857143 = 1.885768398 Simplifying x + 1.642857143 = 1.885768398 Reorder the terms: 1.642857143 + x = 1.885768398 Solving 1.642857143 + x = 1.885768398 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 = 1.885768398 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = 1.885768398 + -1.642857143 x = 1.885768398 + -1.642857143 Combine like terms: 1.885768398 + -1.642857143 = 0.242911255 x = 0.242911255 Simplifying x = 0.242911255Subproblem 2
x + 1.642857143 = -1.885768398 Simplifying x + 1.642857143 = -1.885768398 Reorder the terms: 1.642857143 + x = -1.885768398 Solving 1.642857143 + x = -1.885768398 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 = -1.885768398 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = -1.885768398 + -1.642857143 x = -1.885768398 + -1.642857143 Combine like terms: -1.885768398 + -1.642857143 = -3.528625541 x = -3.528625541 Simplifying x = -3.528625541Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.242911255, -3.528625541}
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