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Simplifying 108 = -5.01x + 4.9x2 Solving 108 = -5.01x + 4.9x2 Solving for variable 'x'. Reorder the terms: 108 + 5.01x + -4.9x2 = -5.01x + 5.01x + 4.9x2 + -4.9x2 Combine like terms: -5.01x + 5.01x = 0.00 108 + 5.01x + -4.9x2 = 0.00 + 4.9x2 + -4.9x2 108 + 5.01x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 108 + 5.01x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -22.04081633 + -1.02244898x + x2 = 0 Move the constant term to the right: Add '22.04081633' to each side of the equation. -22.04081633 + -1.02244898x + 22.04081633 + x2 = 0 + 22.04081633 Reorder the terms: -22.04081633 + 22.04081633 + -1.02244898x + x2 = 0 + 22.04081633 Combine like terms: -22.04081633 + 22.04081633 = 0.00000000 0.00000000 + -1.02244898x + x2 = 0 + 22.04081633 -1.02244898x + x2 = 0 + 22.04081633 Combine like terms: 0 + 22.04081633 = 22.04081633 -1.02244898x + x2 = 22.04081633 The x term is -1.02244898x. Take half its coefficient (-0.51122449). Square it (0.2613504792) and add it to both sides. Add '0.2613504792' to each side of the equation. -1.02244898x + 0.2613504792 + x2 = 22.04081633 + 0.2613504792 Reorder the terms: 0.2613504792 + -1.02244898x + x2 = 22.04081633 + 0.2613504792 Combine like terms: 22.04081633 + 0.2613504792 = 22.3021668092 0.2613504792 + -1.02244898x + x2 = 22.3021668092 Factor a perfect square on the left side: (x + -0.51122449)(x + -0.51122449) = 22.3021668092 Calculate the square root of the right side: 4.722516999 Break this problem into two subproblems by setting (x + -0.51122449) equal to 4.722516999 and -4.722516999.Subproblem 1
x + -0.51122449 = 4.722516999 Simplifying x + -0.51122449 = 4.722516999 Reorder the terms: -0.51122449 + x = 4.722516999 Solving -0.51122449 + x = 4.722516999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.51122449' to each side of the equation. -0.51122449 + 0.51122449 + x = 4.722516999 + 0.51122449 Combine like terms: -0.51122449 + 0.51122449 = 0.00000000 0.00000000 + x = 4.722516999 + 0.51122449 x = 4.722516999 + 0.51122449 Combine like terms: 4.722516999 + 0.51122449 = 5.233741489 x = 5.233741489 Simplifying x = 5.233741489Subproblem 2
x + -0.51122449 = -4.722516999 Simplifying x + -0.51122449 = -4.722516999 Reorder the terms: -0.51122449 + x = -4.722516999 Solving -0.51122449 + x = -4.722516999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.51122449' to each side of the equation. -0.51122449 + 0.51122449 + x = -4.722516999 + 0.51122449 Combine like terms: -0.51122449 + 0.51122449 = 0.00000000 0.00000000 + x = -4.722516999 + 0.51122449 x = -4.722516999 + 0.51122449 Combine like terms: -4.722516999 + 0.51122449 = -4.211292509 x = -4.211292509 Simplifying x = -4.211292509Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.233741489, -4.211292509}
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