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Simplifying -0.01x2 + 1.18x + 2 = 0 Reorder the terms: 2 + 1.18x + -0.01x2 = 0 Solving 2 + 1.18x + -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'. -200 + -118x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -118x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -118x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -118x + x2 = 0 + 200 -118x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -118x + x2 = 200 The x term is -118x. Take half its coefficient (-59). Square it (3481) and add it to both sides. Add '3481' to each side of the equation. -118x + 3481 + x2 = 200 + 3481 Reorder the terms: 3481 + -118x + x2 = 200 + 3481 Combine like terms: 200 + 3481 = 3681 3481 + -118x + x2 = 3681 Factor a perfect square on the left side: (x + -59)(x + -59) = 3681 Calculate the square root of the right side: 60.671245248 Break this problem into two subproblems by setting (x + -59) equal to 60.671245248 and -60.671245248.Subproblem 1
x + -59 = 60.671245248 Simplifying x + -59 = 60.671245248 Reorder the terms: -59 + x = 60.671245248 Solving -59 + x = 60.671245248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '59' to each side of the equation. -59 + 59 + x = 60.671245248 + 59 Combine like terms: -59 + 59 = 0 0 + x = 60.671245248 + 59 x = 60.671245248 + 59 Combine like terms: 60.671245248 + 59 = 119.671245248 x = 119.671245248 Simplifying x = 119.671245248Subproblem 2
x + -59 = -60.671245248 Simplifying x + -59 = -60.671245248 Reorder the terms: -59 + x = -60.671245248 Solving -59 + x = -60.671245248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '59' to each side of the equation. -59 + 59 + x = -60.671245248 + 59 Combine like terms: -59 + 59 = 0 0 + x = -60.671245248 + 59 x = -60.671245248 + 59 Combine like terms: -60.671245248 + 59 = -1.671245248 x = -1.671245248 Simplifying x = -1.671245248Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.671245248, -1.671245248}
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