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Simplifying 93 = 201x + -16x2 Solving 93 = 201x + -16x2 Solving for variable 'x'. Reorder the terms: 93 + -201x + 16x2 = 201x + -201x + -16x2 + 16x2 Combine like terms: 201x + -201x = 0 93 + -201x + 16x2 = 0 + -16x2 + 16x2 93 + -201x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 93 + -201x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.8125 + -12.5625x + x2 = 0 Move the constant term to the right: Add '-5.8125' to each side of the equation. 5.8125 + -12.5625x + -5.8125 + x2 = 0 + -5.8125 Reorder the terms: 5.8125 + -5.8125 + -12.5625x + x2 = 0 + -5.8125 Combine like terms: 5.8125 + -5.8125 = 0.0000 0.0000 + -12.5625x + x2 = 0 + -5.8125 -12.5625x + x2 = 0 + -5.8125 Combine like terms: 0 + -5.8125 = -5.8125 -12.5625x + x2 = -5.8125 The x term is -12.5625x. Take half its coefficient (-6.28125). Square it (39.45410156) and add it to both sides. Add '39.45410156' to each side of the equation. -12.5625x + 39.45410156 + x2 = -5.8125 + 39.45410156 Reorder the terms: 39.45410156 + -12.5625x + x2 = -5.8125 + 39.45410156 Combine like terms: -5.8125 + 39.45410156 = 33.64160156 39.45410156 + -12.5625x + x2 = 33.64160156 Factor a perfect square on the left side: (x + -6.28125)(x + -6.28125) = 33.64160156 Calculate the square root of the right side: 5.800138064 Break this problem into two subproblems by setting (x + -6.28125) equal to 5.800138064 and -5.800138064.Subproblem 1
x + -6.28125 = 5.800138064 Simplifying x + -6.28125 = 5.800138064 Reorder the terms: -6.28125 + x = 5.800138064 Solving -6.28125 + x = 5.800138064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.28125' to each side of the equation. -6.28125 + 6.28125 + x = 5.800138064 + 6.28125 Combine like terms: -6.28125 + 6.28125 = 0.00000 0.00000 + x = 5.800138064 + 6.28125 x = 5.800138064 + 6.28125 Combine like terms: 5.800138064 + 6.28125 = 12.081388064 x = 12.081388064 Simplifying x = 12.081388064Subproblem 2
x + -6.28125 = -5.800138064 Simplifying x + -6.28125 = -5.800138064 Reorder the terms: -6.28125 + x = -5.800138064 Solving -6.28125 + x = -5.800138064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.28125' to each side of the equation. -6.28125 + 6.28125 + x = -5.800138064 + 6.28125 Combine like terms: -6.28125 + 6.28125 = 0.00000 0.00000 + x = -5.800138064 + 6.28125 x = -5.800138064 + 6.28125 Combine like terms: -5.800138064 + 6.28125 = 0.481111936 x = 0.481111936 Simplifying x = 0.481111936Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.081388064, 0.481111936}
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