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Simplifying 4x2 + 96x + 192 = 285 Reorder the terms: 192 + 96x + 4x2 = 285 Solving 192 + 96x + 4x2 = 285 Solving for variable 'x'. Reorder the terms: 192 + -285 + 96x + 4x2 = 285 + -285 Combine like terms: 192 + -285 = -93 -93 + 96x + 4x2 = 285 + -285 Combine like terms: 285 + -285 = 0 -93 + 96x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -23.25 + 24x + x2 = 0 Move the constant term to the right: Add '23.25' to each side of the equation. -23.25 + 24x + 23.25 + x2 = 0 + 23.25 Reorder the terms: -23.25 + 23.25 + 24x + x2 = 0 + 23.25 Combine like terms: -23.25 + 23.25 = 0.00 0.00 + 24x + x2 = 0 + 23.25 24x + x2 = 0 + 23.25 Combine like terms: 0 + 23.25 = 23.25 24x + x2 = 23.25 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 = 23.25 + 144 Reorder the terms: 144 + 24x + x2 = 23.25 + 144 Combine like terms: 23.25 + 144 = 167.25 144 + 24x + x2 = 167.25 Factor a perfect square on the left side: (x + 12)(x + 12) = 167.25 Calculate the square root of the right side: 12.932517156 Break this problem into two subproblems by setting (x + 12) equal to 12.932517156 and -12.932517156.Subproblem 1
x + 12 = 12.932517156 Simplifying x + 12 = 12.932517156 Reorder the terms: 12 + x = 12.932517156 Solving 12 + x = 12.932517156 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 = 12.932517156 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.932517156 + -12 x = 12.932517156 + -12 Combine like terms: 12.932517156 + -12 = 0.932517156 x = 0.932517156 Simplifying x = 0.932517156Subproblem 2
x + 12 = -12.932517156 Simplifying x + 12 = -12.932517156 Reorder the terms: 12 + x = -12.932517156 Solving 12 + x = -12.932517156 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 = -12.932517156 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.932517156 + -12 x = -12.932517156 + -12 Combine like terms: -12.932517156 + -12 = -24.932517156 x = -24.932517156 Simplifying x = -24.932517156Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.932517156, -24.932517156}
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