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Simplifying 0 = -4.9x2 + 30x + 0.5 Reorder the terms: 0 = 0.5 + 30x + -4.9x2 Solving 0 = 0.5 + 30x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -0.5 = -0.5 -0.5 + -30x + 4.9x2 = 0.5 + 30x + -4.9x2 + -0.5 + -30x + 4.9x2 Reorder the terms: -0.5 + -30x + 4.9x2 = 0.5 + -0.5 + 30x + -30x + -4.9x2 + 4.9x2 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + -30x + 4.9x2 = 0.0 + 30x + -30x + -4.9x2 + 4.9x2 -0.5 + -30x + 4.9x2 = 30x + -30x + -4.9x2 + 4.9x2 Combine like terms: 30x + -30x = 0 -0.5 + -30x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -0.5 + -30x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -0.5 + -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'. -0.1020408163 + -6.12244898x + x2 = 0 Move the constant term to the right: Add '0.1020408163' to each side of the equation. -0.1020408163 + -6.12244898x + 0.1020408163 + x2 = 0 + 0.1020408163 Reorder the terms: -0.1020408163 + 0.1020408163 + -6.12244898x + x2 = 0 + 0.1020408163 Combine like terms: -0.1020408163 + 0.1020408163 = 0.0000000000 0.0000000000 + -6.12244898x + x2 = 0 + 0.1020408163 -6.12244898x + x2 = 0 + 0.1020408163 Combine like terms: 0 + 0.1020408163 = 0.1020408163 -6.12244898x + x2 = 0.1020408163 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 = 0.1020408163 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898x + x2 = 0.1020408163 + 9.371095378 Combine like terms: 0.1020408163 + 9.371095378 = 9.4731361943 9.371095378 + -6.12244898x + x2 = 9.4731361943 Factor a perfect square on the left side: (x + -3.06122449)(x + -3.06122449) = 9.4731361943 Calculate the square root of the right side: 3.077846032 Break this problem into two subproblems by setting (x + -3.06122449) equal to 3.077846032 and -3.077846032.Subproblem 1
x + -3.06122449 = 3.077846032 Simplifying x + -3.06122449 = 3.077846032 Reorder the terms: -3.06122449 + x = 3.077846032 Solving -3.06122449 + x = 3.077846032 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 = 3.077846032 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = 3.077846032 + 3.06122449 x = 3.077846032 + 3.06122449 Combine like terms: 3.077846032 + 3.06122449 = 6.139070522 x = 6.139070522 Simplifying x = 6.139070522Subproblem 2
x + -3.06122449 = -3.077846032 Simplifying x + -3.06122449 = -3.077846032 Reorder the terms: -3.06122449 + x = -3.077846032 Solving -3.06122449 + x = -3.077846032 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 = -3.077846032 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = -3.077846032 + 3.06122449 x = -3.077846032 + 3.06122449 Combine like terms: -3.077846032 + 3.06122449 = -0.016621542 x = -0.016621542 Simplifying x = -0.016621542Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.139070522, -0.016621542}
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