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Simplifying -4.9x2 + 30x + 3 = 0 Reorder the terms: 3 + 30x + -4.9x2 = 0 Solving 3 + 30x + -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'. -0.612244898 + -6.12244898x + x2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -6.12244898x + 0.612244898 + x2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -6.12244898x + x2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -6.12244898x + x2 = 0 + 0.612244898 -6.12244898x + x2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -6.12244898x + x2 = 0.612244898 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 = 0.612244898 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898x + x2 = 0.612244898 + 9.371095378 Combine like terms: 0.612244898 + 9.371095378 = 9.983340276 9.371095378 + -6.12244898x + x2 = 9.983340276 Factor a perfect square on the left side: (x + -3.06122449)(x + -3.06122449) = 9.983340276 Calculate the square root of the right side: 3.159642429 Break this problem into two subproblems by setting (x + -3.06122449) equal to 3.159642429 and -3.159642429.Subproblem 1
x + -3.06122449 = 3.159642429 Simplifying x + -3.06122449 = 3.159642429 Reorder the terms: -3.06122449 + x = 3.159642429 Solving -3.06122449 + x = 3.159642429 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 = 3.159642429 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = 3.159642429 + 3.06122449 x = 3.159642429 + 3.06122449 Combine like terms: 3.159642429 + 3.06122449 = 6.220866919 x = 6.220866919 Simplifying x = 6.220866919Subproblem 2
x + -3.06122449 = -3.159642429 Simplifying x + -3.06122449 = -3.159642429 Reorder the terms: -3.06122449 + x = -3.159642429 Solving -3.06122449 + x = -3.159642429 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 = -3.159642429 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = -3.159642429 + 3.06122449 x = -3.159642429 + 3.06122449 Combine like terms: -3.159642429 + 3.06122449 = -0.098417939 x = -0.098417939 Simplifying x = -0.098417939Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.220866919, -0.098417939}
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