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Simplifying -0.002x2 + x + 70 = 0 Reorder the terms: 70 + x + -0.002x2 = 0 Solving 70 + x + -0.002x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.002 the coefficient of the squared term: Divide each side by '-0.002'. -35000 + -500x + x2 = 0 Move the constant term to the right: Add '35000' to each side of the equation. -35000 + -500x + 35000 + x2 = 0 + 35000 Reorder the terms: -35000 + 35000 + -500x + x2 = 0 + 35000 Combine like terms: -35000 + 35000 = 0 0 + -500x + x2 = 0 + 35000 -500x + x2 = 0 + 35000 Combine like terms: 0 + 35000 = 35000 -500x + x2 = 35000 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -500x + 0.25 + x2 = 35000 + 0.25 Reorder the terms: 0.25 + -500x + x2 = 35000 + 0.25 Combine like terms: 35000 + 0.25 = 35000.25 0.25 + -500x + x2 = 35000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 35000.25 Calculate the square root of the right side: 187.083537491 Break this problem into two subproblems by setting (x + 0.5) equal to 187.083537491 and -187.083537491.Subproblem 1
x + 0.5 = 187.083537491 Simplifying x + 0.5 = 187.083537491 Reorder the terms: 0.5 + x = 187.083537491 Solving 0.5 + x = 187.083537491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 187.083537491 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 187.083537491 + -0.5 x = 187.083537491 + -0.5 Combine like terms: 187.083537491 + -0.5 = 186.583537491 x = 186.583537491 Simplifying x = 186.583537491Subproblem 2
x + 0.5 = -187.083537491 Simplifying x + 0.5 = -187.083537491 Reorder the terms: 0.5 + x = -187.083537491 Solving 0.5 + x = -187.083537491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -187.083537491 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -187.083537491 + -0.5 x = -187.083537491 + -0.5 Combine like terms: -187.083537491 + -0.5 = -187.583537491 x = -187.583537491 Simplifying x = -187.583537491Solution
The solution to the problem is based on the solutions from the subproblems. x = {186.583537491, -187.583537491}
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