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Simplifying 3x + 4.9x2 = 800 Solving 3x + 4.9x2 = 800 Solving for variable 'x'. Reorder the terms: -800 + 3x + 4.9x2 = 800 + -800 Combine like terms: 800 + -800 = 0 -800 + 3x + 4.9x2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -163.2653061 + 0.612244898x + x2 = 0 Move the constant term to the right: Add '163.2653061' to each side of the equation. -163.2653061 + 0.612244898x + 163.2653061 + x2 = 0 + 163.2653061 Reorder the terms: -163.2653061 + 163.2653061 + 0.612244898x + x2 = 0 + 163.2653061 Combine like terms: -163.2653061 + 163.2653061 = 0.0000000 0.0000000 + 0.612244898x + x2 = 0 + 163.2653061 0.612244898x + x2 = 0 + 163.2653061 Combine like terms: 0 + 163.2653061 = 163.2653061 0.612244898x + x2 = 163.2653061 The x term is 0.612244898x. Take half its coefficient (0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. 0.612244898x + 0.09371095378 + x2 = 163.2653061 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898x + x2 = 163.2653061 + 0.09371095378 Combine like terms: 163.2653061 + 0.09371095378 = 163.35901705378 0.09371095378 + 0.612244898x + x2 = 163.35901705378 Factor a perfect square on the left side: (x + 0.306122449)(x + 0.306122449) = 163.35901705378 Calculate the square root of the right side: 12.781197794 Break this problem into two subproblems by setting (x + 0.306122449) equal to 12.781197794 and -12.781197794.Subproblem 1
x + 0.306122449 = 12.781197794 Simplifying x + 0.306122449 = 12.781197794 Reorder the terms: 0.306122449 + x = 12.781197794 Solving 0.306122449 + x = 12.781197794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + x = 12.781197794 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + x = 12.781197794 + -0.306122449 x = 12.781197794 + -0.306122449 Combine like terms: 12.781197794 + -0.306122449 = 12.475075345 x = 12.475075345 Simplifying x = 12.475075345Subproblem 2
x + 0.306122449 = -12.781197794 Simplifying x + 0.306122449 = -12.781197794 Reorder the terms: 0.306122449 + x = -12.781197794 Solving 0.306122449 + x = -12.781197794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + x = -12.781197794 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + x = -12.781197794 + -0.306122449 x = -12.781197794 + -0.306122449 Combine like terms: -12.781197794 + -0.306122449 = -13.087320243 x = -13.087320243 Simplifying x = -13.087320243Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.475075345, -13.087320243}
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