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Simplifying 0.01x2 + 0.24x + 8 = 9.4 Reorder the terms: 8 + 0.24x + 0.01x2 = 9.4 Solving 8 + 0.24x + 0.01x2 = 9.4 Solving for variable 'x'. Reorder the terms: 8 + -9.4 + 0.24x + 0.01x2 = 9.4 + -9.4 Combine like terms: 8 + -9.4 = -1.4 -1.4 + 0.24x + 0.01x2 = 9.4 + -9.4 Combine like terms: 9.4 + -9.4 = 0.0 -1.4 + 0.24x + 0.01x2 = 0.0 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -140 + 24x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 24x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 24x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 24x + x2 = 0 + 140 24x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 24x + x2 = 140 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 140 + 144 Reorder the terms: 144 + 24x + x2 = 140 + 144 Combine like terms: 140 + 144 = 284 144 + 24x + x2 = 284 Factor a perfect square on the left side: (x + 12)(x + 12) = 284 Calculate the square root of the right side: 16.852299546 Break this problem into two subproblems by setting (x + 12) equal to 16.852299546 and -16.852299546.Subproblem 1
x + 12 = 16.852299546 Simplifying x + 12 = 16.852299546 Reorder the terms: 12 + x = 16.852299546 Solving 12 + x = 16.852299546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 16.852299546 + -12 Combine like terms: 12 + -12 = 0 0 + x = 16.852299546 + -12 x = 16.852299546 + -12 Combine like terms: 16.852299546 + -12 = 4.852299546 x = 4.852299546 Simplifying x = 4.852299546Subproblem 2
x + 12 = -16.852299546 Simplifying x + 12 = -16.852299546 Reorder the terms: 12 + x = -16.852299546 Solving 12 + x = -16.852299546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -16.852299546 + -12 Combine like terms: 12 + -12 = 0 0 + x = -16.852299546 + -12 x = -16.852299546 + -12 Combine like terms: -16.852299546 + -12 = -28.852299546 x = -28.852299546 Simplifying x = -28.852299546Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.852299546, -28.852299546}
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