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Simplifying -0.01x2 + 1.18x + 0.3481 = 0 Reorder the terms: 0.3481 + 1.18x + -0.01x2 = 0 Solving 0.3481 + 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'. -34.81 + -118x + x2 = 0 Move the constant term to the right: Add '34.81' to each side of the equation. -34.81 + -118x + 34.81 + x2 = 0 + 34.81 Reorder the terms: -34.81 + 34.81 + -118x + x2 = 0 + 34.81 Combine like terms: -34.81 + 34.81 = 0.00 0.00 + -118x + x2 = 0 + 34.81 -118x + x2 = 0 + 34.81 Combine like terms: 0 + 34.81 = 34.81 -118x + x2 = 34.81 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 = 34.81 + 3481 Reorder the terms: 3481 + -118x + x2 = 34.81 + 3481 Combine like terms: 34.81 + 3481 = 3515.81 3481 + -118x + x2 = 3515.81 Factor a perfect square on the left side: (x + -59)(x + -59) = 3515.81 Calculate the square root of the right side: 59.294266165 Break this problem into two subproblems by setting (x + -59) equal to 59.294266165 and -59.294266165.Subproblem 1
x + -59 = 59.294266165 Simplifying x + -59 = 59.294266165 Reorder the terms: -59 + x = 59.294266165 Solving -59 + x = 59.294266165 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 = 59.294266165 + 59 Combine like terms: -59 + 59 = 0 0 + x = 59.294266165 + 59 x = 59.294266165 + 59 Combine like terms: 59.294266165 + 59 = 118.294266165 x = 118.294266165 Simplifying x = 118.294266165Subproblem 2
x + -59 = -59.294266165 Simplifying x + -59 = -59.294266165 Reorder the terms: -59 + x = -59.294266165 Solving -59 + x = -59.294266165 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 = -59.294266165 + 59 Combine like terms: -59 + 59 = 0 0 + x = -59.294266165 + 59 x = -59.294266165 + 59 Combine like terms: -59.294266165 + 59 = -0.294266165 x = -0.294266165 Simplifying x = -0.294266165Solution
The solution to the problem is based on the solutions from the subproblems. x = {118.294266165, -0.294266165}
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