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Simplifying -0.01x2 + 0.5x + 6.1 = 0 Reorder the terms: 6.1 + 0.5x + -0.01x2 = 0 Solving 6.1 + 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'. -610 + -50x + x2 = 0 Move the constant term to the right: Add '610' to each side of the equation. -610 + -50x + 610 + x2 = 0 + 610 Reorder the terms: -610 + 610 + -50x + x2 = 0 + 610 Combine like terms: -610 + 610 = 0 0 + -50x + x2 = 0 + 610 -50x + x2 = 0 + 610 Combine like terms: 0 + 610 = 610 -50x + x2 = 610 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 = 610 + 625 Reorder the terms: 625 + -50x + x2 = 610 + 625 Combine like terms: 610 + 625 = 1235 625 + -50x + x2 = 1235 Factor a perfect square on the left side: (x + -25)(x + -25) = 1235 Calculate the square root of the right side: 35.142566782 Break this problem into two subproblems by setting (x + -25) equal to 35.142566782 and -35.142566782.Subproblem 1
x + -25 = 35.142566782 Simplifying x + -25 = 35.142566782 Reorder the terms: -25 + x = 35.142566782 Solving -25 + x = 35.142566782 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 = 35.142566782 + 25 Combine like terms: -25 + 25 = 0 0 + x = 35.142566782 + 25 x = 35.142566782 + 25 Combine like terms: 35.142566782 + 25 = 60.142566782 x = 60.142566782 Simplifying x = 60.142566782Subproblem 2
x + -25 = -35.142566782 Simplifying x + -25 = -35.142566782 Reorder the terms: -25 + x = -35.142566782 Solving -25 + x = -35.142566782 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 = -35.142566782 + 25 Combine like terms: -25 + 25 = 0 0 + x = -35.142566782 + 25 x = -35.142566782 + 25 Combine like terms: -35.142566782 + 25 = -10.142566782 x = -10.142566782 Simplifying x = -10.142566782Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.142566782, -10.142566782}
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