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Simplifying 7x2 + 23x + -48 = 0 Reorder the terms: -48 + 23x + 7x2 = 0 Solving -48 + 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'. -6.857142857 + 3.285714286x + x2 = 0 Move the constant term to the right: Add '6.857142857' to each side of the equation. -6.857142857 + 3.285714286x + 6.857142857 + x2 = 0 + 6.857142857 Reorder the terms: -6.857142857 + 6.857142857 + 3.285714286x + x2 = 0 + 6.857142857 Combine like terms: -6.857142857 + 6.857142857 = 0.000000000 0.000000000 + 3.285714286x + x2 = 0 + 6.857142857 3.285714286x + x2 = 0 + 6.857142857 Combine like terms: 0 + 6.857142857 = 6.857142857 3.285714286x + x2 = 6.857142857 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 = 6.857142857 + 2.698979592 Reorder the terms: 2.698979592 + 3.285714286x + x2 = 6.857142857 + 2.698979592 Combine like terms: 6.857142857 + 2.698979592 = 9.556122449 2.698979592 + 3.285714286x + x2 = 9.556122449 Factor a perfect square on the left side: (x + 1.642857143)(x + 1.642857143) = 9.556122449 Calculate the square root of the right side: 3.091297858 Break this problem into two subproblems by setting (x + 1.642857143) equal to 3.091297858 and -3.091297858.Subproblem 1
x + 1.642857143 = 3.091297858 Simplifying x + 1.642857143 = 3.091297858 Reorder the terms: 1.642857143 + x = 3.091297858 Solving 1.642857143 + x = 3.091297858 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 = 3.091297858 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = 3.091297858 + -1.642857143 x = 3.091297858 + -1.642857143 Combine like terms: 3.091297858 + -1.642857143 = 1.448440715 x = 1.448440715 Simplifying x = 1.448440715Subproblem 2
x + 1.642857143 = -3.091297858 Simplifying x + 1.642857143 = -3.091297858 Reorder the terms: 1.642857143 + x = -3.091297858 Solving 1.642857143 + x = -3.091297858 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 = -3.091297858 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = -3.091297858 + -1.642857143 x = -3.091297858 + -1.642857143 Combine like terms: -3.091297858 + -1.642857143 = -4.734155001 x = -4.734155001 Simplifying x = -4.734155001Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.448440715, -4.734155001}
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