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Simplifying 9.4 = -0.01x2 + 0.21x + 8.60 Reorder the terms: 9.4 = 8.60 + 0.21x + -0.01x2 Solving 9.4 = 8.60 + 0.21x + -0.01x2 Solving for variable 'x'. Combine like terms: 9.4 + -8.60 = 0.8 0.8 + -0.21x + 0.01x2 = 8.60 + 0.21x + -0.01x2 + -8.60 + -0.21x + 0.01x2 Reorder the terms: 0.8 + -0.21x + 0.01x2 = 8.60 + -8.60 + 0.21x + -0.21x + -0.01x2 + 0.01x2 Combine like terms: 8.60 + -8.60 = 0.00 0.8 + -0.21x + 0.01x2 = 0.00 + 0.21x + -0.21x + -0.01x2 + 0.01x2 0.8 + -0.21x + 0.01x2 = 0.21x + -0.21x + -0.01x2 + 0.01x2 Combine like terms: 0.21x + -0.21x = 0.00 0.8 + -0.21x + 0.01x2 = 0.00 + -0.01x2 + 0.01x2 0.8 + -0.21x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 0.8 + -0.21x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 80 + -21x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -21x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -21x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -21x + x2 = 0 + -80 -21x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -21x + x2 = -80 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -80 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -80 + 110.25 Combine like terms: -80 + 110.25 = 30.25 110.25 + -21x + x2 = 30.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 30.25 Calculate the square root of the right side: 5.5 Break this problem into two subproblems by setting (x + -10.5) equal to 5.5 and -5.5.Subproblem 1
x + -10.5 = 5.5 Simplifying x + -10.5 = 5.5 Reorder the terms: -10.5 + x = 5.5 Solving -10.5 + x = 5.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 5.5 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 5.5 + 10.5 x = 5.5 + 10.5 Combine like terms: 5.5 + 10.5 = 16 x = 16 Simplifying x = 16Subproblem 2
x + -10.5 = -5.5 Simplifying x + -10.5 = -5.5 Reorder the terms: -10.5 + x = -5.5 Solving -10.5 + x = -5.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -5.5 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -5.5 + 10.5 x = -5.5 + 10.5 Combine like terms: -5.5 + 10.5 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {16, 5}
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