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Simplifying -20 + 4.9x2 + -30x = 0 Reorder the terms: -20 + -30x + 4.9x2 = 0 Solving -20 + -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'. -4.081632653 + -6.12244898x + x2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + -6.12244898x + 4.081632653 + x2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + -6.12244898x + x2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + -6.12244898x + x2 = 0 + 4.081632653 -6.12244898x + x2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 -6.12244898x + x2 = 4.081632653 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 = 4.081632653 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898x + x2 = 4.081632653 + 9.371095378 Combine like terms: 4.081632653 + 9.371095378 = 13.452728031 9.371095378 + -6.12244898x + x2 = 13.452728031 Factor a perfect square on the left side: (x + -3.06122449)(x + -3.06122449) = 13.452728031 Calculate the square root of the right side: 3.667796073 Break this problem into two subproblems by setting (x + -3.06122449) equal to 3.667796073 and -3.667796073.Subproblem 1
x + -3.06122449 = 3.667796073 Simplifying x + -3.06122449 = 3.667796073 Reorder the terms: -3.06122449 + x = 3.667796073 Solving -3.06122449 + x = 3.667796073 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 = 3.667796073 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = 3.667796073 + 3.06122449 x = 3.667796073 + 3.06122449 Combine like terms: 3.667796073 + 3.06122449 = 6.729020563 x = 6.729020563 Simplifying x = 6.729020563Subproblem 2
x + -3.06122449 = -3.667796073 Simplifying x + -3.06122449 = -3.667796073 Reorder the terms: -3.06122449 + x = -3.667796073 Solving -3.06122449 + x = -3.667796073 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 = -3.667796073 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = -3.667796073 + 3.06122449 x = -3.667796073 + 3.06122449 Combine like terms: -3.667796073 + 3.06122449 = -0.606571583 x = -0.606571583 Simplifying x = -0.606571583Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.729020563, -0.606571583}
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