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Simplifying 0 = -4.9x2 + 107.8x + 200 Reorder the terms: 0 = 200 + 107.8x + -4.9x2 Solving 0 = 200 + 107.8x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -200 = -200 -200 + -107.8x + 4.9x2 = 200 + 107.8x + -4.9x2 + -200 + -107.8x + 4.9x2 Reorder the terms: -200 + -107.8x + 4.9x2 = 200 + -200 + 107.8x + -107.8x + -4.9x2 + 4.9x2 Combine like terms: 200 + -200 = 0 -200 + -107.8x + 4.9x2 = 0 + 107.8x + -107.8x + -4.9x2 + 4.9x2 -200 + -107.8x + 4.9x2 = 107.8x + -107.8x + -4.9x2 + 4.9x2 Combine like terms: 107.8x + -107.8x = 0.0 -200 + -107.8x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -200 + -107.8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -200 + -107.8x + 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'. -40.81632653 + -22x + x2 = 0 Move the constant term to the right: Add '40.81632653' to each side of the equation. -40.81632653 + -22x + 40.81632653 + x2 = 0 + 40.81632653 Reorder the terms: -40.81632653 + 40.81632653 + -22x + x2 = 0 + 40.81632653 Combine like terms: -40.81632653 + 40.81632653 = 0.00000000 0.00000000 + -22x + x2 = 0 + 40.81632653 -22x + x2 = 0 + 40.81632653 Combine like terms: 0 + 40.81632653 = 40.81632653 -22x + x2 = 40.81632653 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = 40.81632653 + 121 Reorder the terms: 121 + -22x + x2 = 40.81632653 + 121 Combine like terms: 40.81632653 + 121 = 161.81632653 121 + -22x + x2 = 161.81632653 Factor a perfect square on the left side: (x + -11)(x + -11) = 161.81632653 Calculate the square root of the right side: 12.72070464 Break this problem into two subproblems by setting (x + -11) equal to 12.72070464 and -12.72070464.Subproblem 1
x + -11 = 12.72070464 Simplifying x + -11 = 12.72070464 Reorder the terms: -11 + x = 12.72070464 Solving -11 + x = 12.72070464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 12.72070464 + 11 Combine like terms: -11 + 11 = 0 0 + x = 12.72070464 + 11 x = 12.72070464 + 11 Combine like terms: 12.72070464 + 11 = 23.72070464 x = 23.72070464 Simplifying x = 23.72070464Subproblem 2
x + -11 = -12.72070464 Simplifying x + -11 = -12.72070464 Reorder the terms: -11 + x = -12.72070464 Solving -11 + x = -12.72070464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -12.72070464 + 11 Combine like terms: -11 + 11 = 0 0 + x = -12.72070464 + 11 x = -12.72070464 + 11 Combine like terms: -12.72070464 + 11 = -1.72070464 x = -1.72070464 Simplifying x = -1.72070464Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.72070464, -1.72070464}
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