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Simplifying 3 = 0.5x2 + -4x + 9 Reorder the terms: 3 = 9 + -4x + 0.5x2 Solving 3 = 9 + -4x + 0.5x2 Solving for variable 'x'. Combine like terms: 3 + -9 = -6 -6 + 4x + -0.5x2 = 9 + -4x + 0.5x2 + -9 + 4x + -0.5x2 Reorder the terms: -6 + 4x + -0.5x2 = 9 + -9 + -4x + 4x + 0.5x2 + -0.5x2 Combine like terms: 9 + -9 = 0 -6 + 4x + -0.5x2 = 0 + -4x + 4x + 0.5x2 + -0.5x2 -6 + 4x + -0.5x2 = -4x + 4x + 0.5x2 + -0.5x2 Combine like terms: -4x + 4x = 0 -6 + 4x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -6 + 4x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -6 + 4x + -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'. 12 + -8x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -8x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -8x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -8x + x2 = 0 + -12 -8x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -8x + x2 = -12 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -12 + 16 Reorder the terms: 16 + -8x + x2 = -12 + 16 Combine like terms: -12 + 16 = 4 16 + -8x + x2 = 4 Factor a perfect square on the left side: (x + -4)(x + -4) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -4) equal to 2 and -2.Subproblem 1
x + -4 = 2 Simplifying x + -4 = 2 Reorder the terms: -4 + x = 2 Solving -4 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2 + 4 x = 2 + 4 Combine like terms: 2 + 4 = 6 x = 6 Simplifying x = 6Subproblem 2
x + -4 = -2 Simplifying x + -4 = -2 Reorder the terms: -4 + x = -2 Solving -4 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2 + 4 x = -2 + 4 Combine like terms: -2 + 4 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, 2}
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