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Simplifying 162 = 12x + 0.5x2 Solving 162 = 12x + 0.5x2 Solving for variable 'x'. Reorder the terms: 162 + -12x + -0.5x2 = 12x + -12x + 0.5x2 + -0.5x2 Combine like terms: 12x + -12x = 0 162 + -12x + -0.5x2 = 0 + 0.5x2 + -0.5x2 162 + -12x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 162 + -12x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -324 + 24x + x2 = 0 Move the constant term to the right: Add '324' to each side of the equation. -324 + 24x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + 24x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 24x + x2 = 0 + 324 24x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 24x + x2 = 324 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 = 324 + 144 Reorder the terms: 144 + 24x + x2 = 324 + 144 Combine like terms: 324 + 144 = 468 144 + 24x + x2 = 468 Factor a perfect square on the left side: (x + 12)(x + 12) = 468 Calculate the square root of the right side: 21.633307653 Break this problem into two subproblems by setting (x + 12) equal to 21.633307653 and -21.633307653.Subproblem 1
x + 12 = 21.633307653 Simplifying x + 12 = 21.633307653 Reorder the terms: 12 + x = 21.633307653 Solving 12 + x = 21.633307653 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 = 21.633307653 + -12 Combine like terms: 12 + -12 = 0 0 + x = 21.633307653 + -12 x = 21.633307653 + -12 Combine like terms: 21.633307653 + -12 = 9.633307653 x = 9.633307653 Simplifying x = 9.633307653Subproblem 2
x + 12 = -21.633307653 Simplifying x + 12 = -21.633307653 Reorder the terms: 12 + x = -21.633307653 Solving 12 + x = -21.633307653 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 = -21.633307653 + -12 Combine like terms: 12 + -12 = 0 0 + x = -21.633307653 + -12 x = -21.633307653 + -12 Combine like terms: -21.633307653 + -12 = -33.633307653 x = -33.633307653 Simplifying x = -33.633307653Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.633307653, -33.633307653}
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