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Simplifying -0.01x2 + 0.8x + 5.5 = 0 Reorder the terms: 5.5 + 0.8x + -0.01x2 = 0 Solving 5.5 + 0.8x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -550 + -80x + x2 = 0 Move the constant term to the right: Add '550' to each side of the equation. -550 + -80x + 550 + x2 = 0 + 550 Reorder the terms: -550 + 550 + -80x + x2 = 0 + 550 Combine like terms: -550 + 550 = 0 0 + -80x + x2 = 0 + 550 -80x + x2 = 0 + 550 Combine like terms: 0 + 550 = 550 -80x + x2 = 550 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = 550 + 1600 Reorder the terms: 1600 + -80x + x2 = 550 + 1600 Combine like terms: 550 + 1600 = 2150 1600 + -80x + x2 = 2150 Factor a perfect square on the left side: (x + -40)(x + -40) = 2150 Calculate the square root of the right side: 46.368092477 Break this problem into two subproblems by setting (x + -40) equal to 46.368092477 and -46.368092477.Subproblem 1
x + -40 = 46.368092477 Simplifying x + -40 = 46.368092477 Reorder the terms: -40 + x = 46.368092477 Solving -40 + x = 46.368092477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 46.368092477 + 40 Combine like terms: -40 + 40 = 0 0 + x = 46.368092477 + 40 x = 46.368092477 + 40 Combine like terms: 46.368092477 + 40 = 86.368092477 x = 86.368092477 Simplifying x = 86.368092477Subproblem 2
x + -40 = -46.368092477 Simplifying x + -40 = -46.368092477 Reorder the terms: -40 + x = -46.368092477 Solving -40 + x = -46.368092477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -46.368092477 + 40 Combine like terms: -40 + 40 = 0 0 + x = -46.368092477 + 40 x = -46.368092477 + 40 Combine like terms: -46.368092477 + 40 = -6.368092477 x = -6.368092477 Simplifying x = -6.368092477Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.368092477, -6.368092477}
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