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Simplifying 0.99x2 + -1x + -60 = 0 Reorder the terms: -60 + -1x + 0.99x2 = 0 Solving -60 + -1x + 0.99x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.99 the coefficient of the squared term: Divide each side by '0.99'. -60.60606061 + -1.01010101x + x2 = 0 Move the constant term to the right: Add '60.60606061' to each side of the equation. -60.60606061 + -1.01010101x + 60.60606061 + x2 = 0 + 60.60606061 Reorder the terms: -60.60606061 + 60.60606061 + -1.01010101x + x2 = 0 + 60.60606061 Combine like terms: -60.60606061 + 60.60606061 = 0.00000000 0.00000000 + -1.01010101x + x2 = 0 + 60.60606061 -1.01010101x + x2 = 0 + 60.60606061 Combine like terms: 0 + 60.60606061 = 60.60606061 -1.01010101x + x2 = 60.60606061 The x term is -1.01010101x. Take half its coefficient (-0.505050505). Square it (0.2550760126) and add it to both sides. Add '0.2550760126' to each side of the equation. -1.01010101x + 0.2550760126 + x2 = 60.60606061 + 0.2550760126 Reorder the terms: 0.2550760126 + -1.01010101x + x2 = 60.60606061 + 0.2550760126 Combine like terms: 60.60606061 + 0.2550760126 = 60.8611366226 0.2550760126 + -1.01010101x + x2 = 60.8611366226 Factor a perfect square on the left side: (x + -0.505050505)(x + -0.505050505) = 60.8611366226 Calculate the square root of the right side: 7.801354794 Break this problem into two subproblems by setting (x + -0.505050505) equal to 7.801354794 and -7.801354794.Subproblem 1
x + -0.505050505 = 7.801354794 Simplifying x + -0.505050505 = 7.801354794 Reorder the terms: -0.505050505 + x = 7.801354794 Solving -0.505050505 + x = 7.801354794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.505050505' to each side of the equation. -0.505050505 + 0.505050505 + x = 7.801354794 + 0.505050505 Combine like terms: -0.505050505 + 0.505050505 = 0.000000000 0.000000000 + x = 7.801354794 + 0.505050505 x = 7.801354794 + 0.505050505 Combine like terms: 7.801354794 + 0.505050505 = 8.306405299 x = 8.306405299 Simplifying x = 8.306405299Subproblem 2
x + -0.505050505 = -7.801354794 Simplifying x + -0.505050505 = -7.801354794 Reorder the terms: -0.505050505 + x = -7.801354794 Solving -0.505050505 + x = -7.801354794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.505050505' to each side of the equation. -0.505050505 + 0.505050505 + x = -7.801354794 + 0.505050505 Combine like terms: -0.505050505 + 0.505050505 = 0.000000000 0.000000000 + x = -7.801354794 + 0.505050505 x = -7.801354794 + 0.505050505 Combine like terms: -7.801354794 + 0.505050505 = -7.296304289 x = -7.296304289 Simplifying x = -7.296304289Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.306405299, -7.296304289}
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