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Simplifying 7.13x2 + 102.76x + 291.3792 = 0 Reorder the terms: 291.3792 + 102.76x + 7.13x2 = 0 Solving 291.3792 + 102.76x + 7.13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7.13 the coefficient of the squared term: Divide each side by '7.13'. 40.86664797 + 14.41234222x + x2 = 0 Move the constant term to the right: Add '-40.86664797' to each side of the equation. 40.86664797 + 14.41234222x + -40.86664797 + x2 = 0 + -40.86664797 Reorder the terms: 40.86664797 + -40.86664797 + 14.41234222x + x2 = 0 + -40.86664797 Combine like terms: 40.86664797 + -40.86664797 = 0.00000000 0.00000000 + 14.41234222x + x2 = 0 + -40.86664797 14.41234222x + x2 = 0 + -40.86664797 Combine like terms: 0 + -40.86664797 = -40.86664797 14.41234222x + x2 = -40.86664797 The x term is 14.41234222x. Take half its coefficient (7.20617111). Square it (51.92890207) and add it to both sides. Add '51.92890207' to each side of the equation. 14.41234222x + 51.92890207 + x2 = -40.86664797 + 51.92890207 Reorder the terms: 51.92890207 + 14.41234222x + x2 = -40.86664797 + 51.92890207 Combine like terms: -40.86664797 + 51.92890207 = 11.0622541 51.92890207 + 14.41234222x + x2 = 11.0622541 Factor a perfect square on the left side: (x + 7.20617111)(x + 7.20617111) = 11.0622541 Calculate the square root of the right side: 3.325996708 Break this problem into two subproblems by setting (x + 7.20617111) equal to 3.325996708 and -3.325996708.Subproblem 1
x + 7.20617111 = 3.325996708 Simplifying x + 7.20617111 = 3.325996708 Reorder the terms: 7.20617111 + x = 3.325996708 Solving 7.20617111 + x = 3.325996708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.20617111' to each side of the equation. 7.20617111 + -7.20617111 + x = 3.325996708 + -7.20617111 Combine like terms: 7.20617111 + -7.20617111 = 0.00000000 0.00000000 + x = 3.325996708 + -7.20617111 x = 3.325996708 + -7.20617111 Combine like terms: 3.325996708 + -7.20617111 = -3.880174402 x = -3.880174402 Simplifying x = -3.880174402Subproblem 2
x + 7.20617111 = -3.325996708 Simplifying x + 7.20617111 = -3.325996708 Reorder the terms: 7.20617111 + x = -3.325996708 Solving 7.20617111 + x = -3.325996708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.20617111' to each side of the equation. 7.20617111 + -7.20617111 + x = -3.325996708 + -7.20617111 Combine like terms: 7.20617111 + -7.20617111 = 0.00000000 0.00000000 + x = -3.325996708 + -7.20617111 x = -3.325996708 + -7.20617111 Combine like terms: -3.325996708 + -7.20617111 = -10.532167818 x = -10.532167818 Simplifying x = -10.532167818Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.880174402, -10.532167818}
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