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Simplifying -0.5x2 + 3x + 4 = -4 Reorder the terms: 4 + 3x + -0.5x2 = -4 Solving 4 + 3x + -0.5x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + 4 + 3x + -0.5x2 = -4 + 4 Combine like terms: 4 + 4 = 8 8 + 3x + -0.5x2 = -4 + 4 Combine like terms: -4 + 4 = 0 8 + 3x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -16 + -6x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -6x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -6x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -6x + x2 = 0 + 16 -6x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -6x + x2 = 16 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 16 + 9 Reorder the terms: 9 + -6x + x2 = 16 + 9 Combine like terms: 16 + 9 = 25 9 + -6x + x2 = 25 Factor a perfect square on the left side: (x + -3)(x + -3) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + -3) equal to 5 and -5.Subproblem 1
x + -3 = 5 Simplifying x + -3 = 5 Reorder the terms: -3 + x = 5 Solving -3 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5 + 3 x = 5 + 3 Combine like terms: 5 + 3 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -3 = -5 Simplifying x + -3 = -5 Reorder the terms: -3 + x = -5 Solving -3 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5 + 3 x = -5 + 3 Combine like terms: -5 + 3 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -2}
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