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Simplifying 98.5 = (-4.9x2) + 49x Reorder the terms: 98.5 = 49x + (-4.9x2) Solving 98.5 = 49x + (-4.9x2) Solving for variable 'x'. Reorder the terms: 98.5 + -49x + (4.9x2) = 49x + -49x + (-4.9x2) + (4.9x2) Combine like terms: 49x + -49x = 0 98.5 + -49x + (4.9x2) = 0 + (-4.9x2) + (4.9x2) 98.5 + -49x + (4.9x2) = (-4.9x2) + (4.9x2) Combine like terms: (-4.9x2) + (4.9x2) = 0.0 98.5 + -49x + (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'. 20.10204082 + -10x + x2 = 0 Move the constant term to the right: Add '-20.10204082' to each side of the equation. 20.10204082 + -10x + -20.10204082 + x2 = 0 + -20.10204082 Reorder the terms: 20.10204082 + -20.10204082 + -10x + x2 = 0 + -20.10204082 Combine like terms: 20.10204082 + -20.10204082 = 0.00000000 0.00000000 + -10x + x2 = 0 + -20.10204082 -10x + x2 = 0 + -20.10204082 Combine like terms: 0 + -20.10204082 = -20.10204082 -10x + x2 = -20.10204082 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -20.10204082 + 25 Reorder the terms: 25 + -10x + x2 = -20.10204082 + 25 Combine like terms: -20.10204082 + 25 = 4.89795918 25 + -10x + x2 = 4.89795918 Factor a perfect square on the left side: ((x) + -5)((x) + -5) = 4.89795918 Calculate the square root of the right side: 2.21313334 Break this problem into two subproblems by setting ((x) + -5) equal to 2.21313334 and -2.21313334.Subproblem 1
(x) + -5 = 2.21313334 Simplifying (x) + -5 = 2.21313334 x + -5 = 2.21313334 Reorder the terms: -5 + x = 2.21313334 Solving -5 + x = 2.21313334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.21313334 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.21313334 + 5 x = 2.21313334 + 5 Combine like terms: 2.21313334 + 5 = 7.21313334 x = 7.21313334 Simplifying x = 7.21313334Subproblem 2
(x) + -5 = -2.21313334 Simplifying (x) + -5 = -2.21313334 x + -5 = -2.21313334 Reorder the terms: -5 + x = -2.21313334 Solving -5 + x = -2.21313334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.21313334 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.21313334 + 5 x = -2.21313334 + 5 Combine like terms: -2.21313334 + 5 = 2.78686666 x = 2.78686666 Simplifying x = 2.78686666Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.21313334, 2.78686666}
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