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Simplifying (-0.01x2) + 0.6x + 6.1 = 0 Reorder the terms: 6.1 + 0.6x + (-0.01x2) = 0 Solving 6.1 + 0.6x + (-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 + -60x + x2 = 0 Move the constant term to the right: Add '610' to each side of the equation. -610 + -60x + 610 + x2 = 0 + 610 Reorder the terms: -610 + 610 + -60x + x2 = 0 + 610 Combine like terms: -610 + 610 = 0 0 + -60x + x2 = 0 + 610 -60x + x2 = 0 + 610 Combine like terms: 0 + 610 = 610 -60x + x2 = 610 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = 610 + 900 Reorder the terms: 900 + -60x + x2 = 610 + 900 Combine like terms: 610 + 900 = 1510 900 + -60x + x2 = 1510 Factor a perfect square on the left side: ((x) + -30)((x) + -30) = 1510 Calculate the square root of the right side: 38.858718455 Break this problem into two subproblems by setting ((x) + -30) equal to 38.858718455 and -38.858718455.Subproblem 1
(x) + -30 = 38.858718455 Simplifying (x) + -30 = 38.858718455 x + -30 = 38.858718455 Reorder the terms: -30 + x = 38.858718455 Solving -30 + x = 38.858718455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 38.858718455 + 30 Combine like terms: -30 + 30 = 0 0 + x = 38.858718455 + 30 x = 38.858718455 + 30 Combine like terms: 38.858718455 + 30 = 68.858718455 x = 68.858718455 Simplifying x = 68.858718455Subproblem 2
(x) + -30 = -38.858718455 Simplifying (x) + -30 = -38.858718455 x + -30 = -38.858718455 Reorder the terms: -30 + x = -38.858718455 Solving -30 + x = -38.858718455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -38.858718455 + 30 Combine like terms: -30 + 30 = 0 0 + x = -38.858718455 + 30 x = -38.858718455 + 30 Combine like terms: -38.858718455 + 30 = -8.858718455 x = -8.858718455 Simplifying x = -8.858718455Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.858718455, -8.858718455}
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