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Simplifying -16x2 + -29x + 200 = 0 Reorder the terms: 200 + -29x + -16x2 = 0 Solving 200 + -29x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -12.5 + 1.8125x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 1.8125x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 1.8125x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 1.8125x + x2 = 0 + 12.5 1.8125x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 1.8125x + x2 = 12.5 The x term is 1.8125x. Take half its coefficient (0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. 1.8125x + 0.8212890625 + x2 = 12.5 + 0.8212890625 Reorder the terms: 0.8212890625 + 1.8125x + x2 = 12.5 + 0.8212890625 Combine like terms: 12.5 + 0.8212890625 = 13.3212890625 0.8212890625 + 1.8125x + x2 = 13.3212890625 Factor a perfect square on the left side: (x + 0.90625)(x + 0.90625) = 13.3212890625 Calculate the square root of the right side: 3.649834114 Break this problem into two subproblems by setting (x + 0.90625) equal to 3.649834114 and -3.649834114.Subproblem 1
x + 0.90625 = 3.649834114 Simplifying x + 0.90625 = 3.649834114 Reorder the terms: 0.90625 + x = 3.649834114 Solving 0.90625 + x = 3.649834114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + x = 3.649834114 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + x = 3.649834114 + -0.90625 x = 3.649834114 + -0.90625 Combine like terms: 3.649834114 + -0.90625 = 2.743584114 x = 2.743584114 Simplifying x = 2.743584114Subproblem 2
x + 0.90625 = -3.649834114 Simplifying x + 0.90625 = -3.649834114 Reorder the terms: 0.90625 + x = -3.649834114 Solving 0.90625 + x = -3.649834114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + x = -3.649834114 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + x = -3.649834114 + -0.90625 x = -3.649834114 + -0.90625 Combine like terms: -3.649834114 + -0.90625 = -4.556084114 x = -4.556084114 Simplifying x = -4.556084114Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.743584114, -4.556084114}
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