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Simplifying 0 = -0.25x2 + 6x + -27 Reorder the terms: 0 = -27 + 6x + -0.25x2 Solving 0 = -27 + 6x + -0.25x2 Solving for variable 'x'. Combine like terms: 0 + 27 = 27 27 + -6x + 0.25x2 = -27 + 6x + -0.25x2 + 27 + -6x + 0.25x2 Reorder the terms: 27 + -6x + 0.25x2 = -27 + 27 + 6x + -6x + -0.25x2 + 0.25x2 Combine like terms: -27 + 27 = 0 27 + -6x + 0.25x2 = 0 + 6x + -6x + -0.25x2 + 0.25x2 27 + -6x + 0.25x2 = 6x + -6x + -0.25x2 + 0.25x2 Combine like terms: 6x + -6x = 0 27 + -6x + 0.25x2 = 0 + -0.25x2 + 0.25x2 27 + -6x + 0.25x2 = -0.25x2 + 0.25x2 Combine like terms: -0.25x2 + 0.25x2 = 0.00 27 + -6x + 0.25x2 = 0.00 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 108 + -24x + x2 = 0 Move the constant term to the right: Add '-108' to each side of the equation. 108 + -24x + -108 + x2 = 0 + -108 Reorder the terms: 108 + -108 + -24x + x2 = 0 + -108 Combine like terms: 108 + -108 = 0 0 + -24x + x2 = 0 + -108 -24x + x2 = 0 + -108 Combine like terms: 0 + -108 = -108 -24x + x2 = -108 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 = -108 + 144 Reorder the terms: 144 + -24x + x2 = -108 + 144 Combine like terms: -108 + 144 = 36 144 + -24x + x2 = 36 Factor a perfect square on the left side: (x + -12)(x + -12) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + -12) equal to 6 and -6.Subproblem 1
x + -12 = 6 Simplifying x + -12 = 6 Reorder the terms: -12 + x = 6 Solving -12 + x = 6 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 = 6 + 12 Combine like terms: -12 + 12 = 0 0 + x = 6 + 12 x = 6 + 12 Combine like terms: 6 + 12 = 18 x = 18 Simplifying x = 18Subproblem 2
x + -12 = -6 Simplifying x + -12 = -6 Reorder the terms: -12 + x = -6 Solving -12 + x = -6 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 = -6 + 12 Combine like terms: -12 + 12 = 0 0 + x = -6 + 12 x = -6 + 12 Combine like terms: -6 + 12 = 6 x = 6 Simplifying x = 6Solution
The solution to the problem is based on the solutions from the subproblems. x = {18, 6}
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