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Simplifying 0 = 4.9x2 + 30x + 19 Reorder the terms: 0 = 19 + 30x + 4.9x2 Solving 0 = 19 + 30x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + -19 = -19 -19 + -30x + -4.9x2 = 19 + 30x + 4.9x2 + -19 + -30x + -4.9x2 Reorder the terms: -19 + -30x + -4.9x2 = 19 + -19 + 30x + -30x + 4.9x2 + -4.9x2 Combine like terms: 19 + -19 = 0 -19 + -30x + -4.9x2 = 0 + 30x + -30x + 4.9x2 + -4.9x2 -19 + -30x + -4.9x2 = 30x + -30x + 4.9x2 + -4.9x2 Combine like terms: 30x + -30x = 0 -19 + -30x + -4.9x2 = 0 + 4.9x2 + -4.9x2 -19 + -30x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 -19 + -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'. 3.87755102 + 6.12244898x + x2 = 0 Move the constant term to the right: Add '-3.87755102' to each side of the equation. 3.87755102 + 6.12244898x + -3.87755102 + x2 = 0 + -3.87755102 Reorder the terms: 3.87755102 + -3.87755102 + 6.12244898x + x2 = 0 + -3.87755102 Combine like terms: 3.87755102 + -3.87755102 = 0.00000000 0.00000000 + 6.12244898x + x2 = 0 + -3.87755102 6.12244898x + x2 = 0 + -3.87755102 Combine like terms: 0 + -3.87755102 = -3.87755102 6.12244898x + x2 = -3.87755102 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 = -3.87755102 + 9.371095378 Reorder the terms: 9.371095378 + 6.12244898x + x2 = -3.87755102 + 9.371095378 Combine like terms: -3.87755102 + 9.371095378 = 5.493544358 9.371095378 + 6.12244898x + x2 = 5.493544358 Factor a perfect square on the left side: (x + 3.06122449)(x + 3.06122449) = 5.493544358 Calculate the square root of the right side: 2.343831128 Break this problem into two subproblems by setting (x + 3.06122449) equal to 2.343831128 and -2.343831128.Subproblem 1
x + 3.06122449 = 2.343831128 Simplifying x + 3.06122449 = 2.343831128 Reorder the terms: 3.06122449 + x = 2.343831128 Solving 3.06122449 + x = 2.343831128 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 = 2.343831128 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + x = 2.343831128 + -3.06122449 x = 2.343831128 + -3.06122449 Combine like terms: 2.343831128 + -3.06122449 = -0.717393362 x = -0.717393362 Simplifying x = -0.717393362Subproblem 2
x + 3.06122449 = -2.343831128 Simplifying x + 3.06122449 = -2.343831128 Reorder the terms: 3.06122449 + x = -2.343831128 Solving 3.06122449 + x = -2.343831128 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 = -2.343831128 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + x = -2.343831128 + -3.06122449 x = -2.343831128 + -3.06122449 Combine like terms: -2.343831128 + -3.06122449 = -5.405055618 x = -5.405055618 Simplifying x = -5.405055618Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.717393362, -5.405055618}
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