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Simplifying -0.01x2 + 0.5x + 5.9 = 0 Reorder the terms: 5.9 + 0.5x + -0.01x2 = 0 Solving 5.9 + 0.5x + -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'. -590 + -50x + x2 = 0 Move the constant term to the right: Add '590' to each side of the equation. -590 + -50x + 590 + x2 = 0 + 590 Reorder the terms: -590 + 590 + -50x + x2 = 0 + 590 Combine like terms: -590 + 590 = 0 0 + -50x + x2 = 0 + 590 -50x + x2 = 0 + 590 Combine like terms: 0 + 590 = 590 -50x + x2 = 590 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 590 + 625 Reorder the terms: 625 + -50x + x2 = 590 + 625 Combine like terms: 590 + 625 = 1215 625 + -50x + x2 = 1215 Factor a perfect square on the left side: (x + -25)(x + -25) = 1215 Calculate the square root of the right side: 34.856850116 Break this problem into two subproblems by setting (x + -25) equal to 34.856850116 and -34.856850116.Subproblem 1
x + -25 = 34.856850116 Simplifying x + -25 = 34.856850116 Reorder the terms: -25 + x = 34.856850116 Solving -25 + x = 34.856850116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 34.856850116 + 25 Combine like terms: -25 + 25 = 0 0 + x = 34.856850116 + 25 x = 34.856850116 + 25 Combine like terms: 34.856850116 + 25 = 59.856850116 x = 59.856850116 Simplifying x = 59.856850116Subproblem 2
x + -25 = -34.856850116 Simplifying x + -25 = -34.856850116 Reorder the terms: -25 + x = -34.856850116 Solving -25 + x = -34.856850116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -34.856850116 + 25 Combine like terms: -25 + 25 = 0 0 + x = -34.856850116 + 25 x = -34.856850116 + 25 Combine like terms: -34.856850116 + 25 = -9.856850116 x = -9.856850116 Simplifying x = -9.856850116Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.856850116, -9.856850116}
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