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Simplifying 8X + -0.1X2 + -5 = 0 Reorder the terms: -5 + 8X + -0.1X2 = 0 Solving -5 + 8X + -0.1X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 50 + -80X + X2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -80X + -50 + X2 = 0 + -50 Reorder the terms: 50 + -50 + -80X + X2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -80X + X2 = 0 + -50 -80X + X2 = 0 + -50 Combine like terms: 0 + -50 = -50 -80X + X2 = -50 The X term is -80X. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80X + 1600 + X2 = -50 + 1600 Reorder the terms: 1600 + -80X + X2 = -50 + 1600 Combine like terms: -50 + 1600 = 1550 1600 + -80X + X2 = 1550 Factor a perfect square on the left side: (X + -40)(X + -40) = 1550 Calculate the square root of the right side: 39.37003937 Break this problem into two subproblems by setting (X + -40) equal to 39.37003937 and -39.37003937.Subproblem 1
X + -40 = 39.37003937 Simplifying X + -40 = 39.37003937 Reorder the terms: -40 + X = 39.37003937 Solving -40 + X = 39.37003937 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + X = 39.37003937 + 40 Combine like terms: -40 + 40 = 0 0 + X = 39.37003937 + 40 X = 39.37003937 + 40 Combine like terms: 39.37003937 + 40 = 79.37003937 X = 79.37003937 Simplifying X = 79.37003937Subproblem 2
X + -40 = -39.37003937 Simplifying X + -40 = -39.37003937 Reorder the terms: -40 + X = -39.37003937 Solving -40 + X = -39.37003937 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + X = -39.37003937 + 40 Combine like terms: -40 + 40 = 0 0 + X = -39.37003937 + 40 X = -39.37003937 + 40 Combine like terms: -39.37003937 + 40 = 0.62996063 X = 0.62996063 Simplifying X = 0.62996063Solution
The solution to the problem is based on the solutions from the subproblems. X = {79.37003937, 0.62996063}
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