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Simplifying -4.9x2 + 30x + 1.4 = 1.7 Reorder the terms: 1.4 + 30x + -4.9x2 = 1.7 Solving 1.4 + 30x + -4.9x2 = 1.7 Solving for variable 'x'. Reorder the terms: 1.4 + -1.7 + 30x + -4.9x2 = 1.7 + -1.7 Combine like terms: 1.4 + -1.7 = -0.3 -0.3 + 30x + -4.9x2 = 1.7 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 -0.3 + 30x + -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'. 0.0612244898 + -6.12244898x + x2 = 0 Move the constant term to the right: Add '-0.0612244898' to each side of the equation. 0.0612244898 + -6.12244898x + -0.0612244898 + x2 = 0 + -0.0612244898 Reorder the terms: 0.0612244898 + -0.0612244898 + -6.12244898x + x2 = 0 + -0.0612244898 Combine like terms: 0.0612244898 + -0.0612244898 = 0.0000000000 0.0000000000 + -6.12244898x + x2 = 0 + -0.0612244898 -6.12244898x + x2 = 0 + -0.0612244898 Combine like terms: 0 + -0.0612244898 = -0.0612244898 -6.12244898x + x2 = -0.0612244898 The x term is -6.12244898x. Take half its coefficient (-3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. -6.12244898x + 9.371095378 + x2 = -0.0612244898 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898x + x2 = -0.0612244898 + 9.371095378 Combine like terms: -0.0612244898 + 9.371095378 = 9.3098708882 9.371095378 + -6.12244898x + x2 = 9.3098708882 Factor a perfect square on the left side: (x + -3.06122449)(x + -3.06122449) = 9.3098708882 Calculate the square root of the right side: 3.051208103 Break this problem into two subproblems by setting (x + -3.06122449) equal to 3.051208103 and -3.051208103.Subproblem 1
x + -3.06122449 = 3.051208103 Simplifying x + -3.06122449 = 3.051208103 Reorder the terms: -3.06122449 + x = 3.051208103 Solving -3.06122449 + x = 3.051208103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + x = 3.051208103 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = 3.051208103 + 3.06122449 x = 3.051208103 + 3.06122449 Combine like terms: 3.051208103 + 3.06122449 = 6.112432593 x = 6.112432593 Simplifying x = 6.112432593Subproblem 2
x + -3.06122449 = -3.051208103 Simplifying x + -3.06122449 = -3.051208103 Reorder the terms: -3.06122449 + x = -3.051208103 Solving -3.06122449 + x = -3.051208103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + x = -3.051208103 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = -3.051208103 + 3.06122449 x = -3.051208103 + 3.06122449 Combine like terms: -3.051208103 + 3.06122449 = 0.010016387 x = 0.010016387 Simplifying x = 0.010016387Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.112432593, 0.010016387}
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