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Simplifying -0.05x2 + 6x + -5 = 0 Reorder the terms: -5 + 6x + -0.05x2 = 0 Solving -5 + 6x + -0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 100 + -120x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -120x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -120x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -120x + x2 = 0 + -100 -120x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -120x + x2 = -100 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = -100 + 3600 Reorder the terms: 3600 + -120x + x2 = -100 + 3600 Combine like terms: -100 + 3600 = 3500 3600 + -120x + x2 = 3500 Factor a perfect square on the left side: (x + -60)(x + -60) = 3500 Calculate the square root of the right side: 59.160797831 Break this problem into two subproblems by setting (x + -60) equal to 59.160797831 and -59.160797831.Subproblem 1
x + -60 = 59.160797831 Simplifying x + -60 = 59.160797831 Reorder the terms: -60 + x = 59.160797831 Solving -60 + x = 59.160797831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 59.160797831 + 60 Combine like terms: -60 + 60 = 0 0 + x = 59.160797831 + 60 x = 59.160797831 + 60 Combine like terms: 59.160797831 + 60 = 119.160797831 x = 119.160797831 Simplifying x = 119.160797831Subproblem 2
x + -60 = -59.160797831 Simplifying x + -60 = -59.160797831 Reorder the terms: -60 + x = -59.160797831 Solving -60 + x = -59.160797831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -59.160797831 + 60 Combine like terms: -60 + 60 = 0 0 + x = -59.160797831 + 60 x = -59.160797831 + 60 Combine like terms: -59.160797831 + 60 = 0.839202169 x = 0.839202169 Simplifying x = 0.839202169Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.160797831, 0.839202169}
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