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Simplifying 2x + 7 = -0.5x2 + -2x + 1 Reorder the terms: 7 + 2x = -0.5x2 + -2x + 1 Reorder the terms: 7 + 2x = 1 + -2x + -0.5x2 Solving 7 + 2x = 1 + -2x + -0.5x2 Solving for variable 'x'. Reorder the terms: 7 + -1 + 2x + 2x + 0.5x2 = 1 + -2x + -0.5x2 + -1 + 2x + 0.5x2 Combine like terms: 7 + -1 = 6 6 + 2x + 2x + 0.5x2 = 1 + -2x + -0.5x2 + -1 + 2x + 0.5x2 Combine like terms: 2x + 2x = 4x 6 + 4x + 0.5x2 = 1 + -2x + -0.5x2 + -1 + 2x + 0.5x2 Reorder the terms: 6 + 4x + 0.5x2 = 1 + -1 + -2x + 2x + -0.5x2 + 0.5x2 Combine like terms: 1 + -1 = 0 6 + 4x + 0.5x2 = 0 + -2x + 2x + -0.5x2 + 0.5x2 6 + 4x + 0.5x2 = -2x + 2x + -0.5x2 + 0.5x2 Combine like terms: -2x + 2x = 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 = -2 x = -2 Simplifying x = -2Subproblem 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 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2, -6}
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