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Simplifying 4.9x2 + 60x + 50 = 0 Reorder the terms: 50 + 60x + 4.9x2 = 0 Solving 50 + 60x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 10.20408163 + 12.24489796x + x2 = 0 Move the constant term to the right: Add '-10.20408163' to each side of the equation. 10.20408163 + 12.24489796x + -10.20408163 + x2 = 0 + -10.20408163 Reorder the terms: 10.20408163 + -10.20408163 + 12.24489796x + x2 = 0 + -10.20408163 Combine like terms: 10.20408163 + -10.20408163 = 0.00000000 0.00000000 + 12.24489796x + x2 = 0 + -10.20408163 12.24489796x + x2 = 0 + -10.20408163 Combine like terms: 0 + -10.20408163 = -10.20408163 12.24489796x + x2 = -10.20408163 The x term is 12.24489796x. Take half its coefficient (6.12244898). Square it (37.48438151) and add it to both sides. Add '37.48438151' to each side of the equation. 12.24489796x + 37.48438151 + x2 = -10.20408163 + 37.48438151 Reorder the terms: 37.48438151 + 12.24489796x + x2 = -10.20408163 + 37.48438151 Combine like terms: -10.20408163 + 37.48438151 = 27.28029988 37.48438151 + 12.24489796x + x2 = 27.28029988 Factor a perfect square on the left side: (x + 6.12244898)(x + 6.12244898) = 27.28029988 Calculate the square root of the right side: 5.22305465 Break this problem into two subproblems by setting (x + 6.12244898) equal to 5.22305465 and -5.22305465.Subproblem 1
x + 6.12244898 = 5.22305465 Simplifying x + 6.12244898 = 5.22305465 Reorder the terms: 6.12244898 + x = 5.22305465 Solving 6.12244898 + x = 5.22305465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.12244898' to each side of the equation. 6.12244898 + -6.12244898 + x = 5.22305465 + -6.12244898 Combine like terms: 6.12244898 + -6.12244898 = 0.00000000 0.00000000 + x = 5.22305465 + -6.12244898 x = 5.22305465 + -6.12244898 Combine like terms: 5.22305465 + -6.12244898 = -0.89939433 x = -0.89939433 Simplifying x = -0.89939433Subproblem 2
x + 6.12244898 = -5.22305465 Simplifying x + 6.12244898 = -5.22305465 Reorder the terms: 6.12244898 + x = -5.22305465 Solving 6.12244898 + x = -5.22305465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.12244898' to each side of the equation. 6.12244898 + -6.12244898 + x = -5.22305465 + -6.12244898 Combine like terms: 6.12244898 + -6.12244898 = 0.00000000 0.00000000 + x = -5.22305465 + -6.12244898 x = -5.22305465 + -6.12244898 Combine like terms: -5.22305465 + -6.12244898 = -11.34550363 x = -11.34550363 Simplifying x = -11.34550363Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.89939433, -11.34550363}
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