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Simplifying 12 = -0.1875x2 + 3x Reorder the terms: 12 = 3x + -0.1875x2 Solving 12 = 3x + -0.1875x2 Solving for variable 'x'. Reorder the terms: 12 + -3x + 0.1875x2 = 3x + -3x + -0.1875x2 + 0.1875x2 Combine like terms: 3x + -3x = 0 12 + -3x + 0.1875x2 = 0 + -0.1875x2 + 0.1875x2 12 + -3x + 0.1875x2 = -0.1875x2 + 0.1875x2 Combine like terms: -0.1875x2 + 0.1875x2 = 0.0000 12 + -3x + 0.1875x2 = 0.0000 Begin completing the square. Divide all terms by 0.1875 the coefficient of the squared term: Divide each side by '0.1875'. 64 + -16x + x2 = 0 Move the constant term to the right: Add '-64' to each side of the equation. 64 + -16x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -16x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -16x + x2 = 0 + -64 -16x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -16x + x2 = -64 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -64 + 64 Reorder the terms: 64 + -16x + x2 = -64 + 64 Combine like terms: -64 + 64 = 0 64 + -16x + x2 = 0 Factor a perfect square on the left side: (x + -8)(x + -8) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -8) equal to 0 and 0.Subproblem 1
x + -8 = 0 Simplifying x + -8 = 0 Reorder the terms: -8 + x = 0 Solving -8 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -8 = 0 Simplifying x + -8 = 0 Reorder the terms: -8 + x = 0 Solving -8 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, 8}
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