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Simplifying x2 + -1x + -15 = 0.5x2 + x + -9 Reorder the terms: -15 + -1x + x2 = 0.5x2 + x + -9 Reorder the terms: -15 + -1x + x2 = -9 + x + 0.5x2 Solving -15 + -1x + x2 = -9 + x + 0.5x2 Solving for variable 'x'. Reorder the terms: -15 + 9 + -1x + -1x + x2 + -0.5x2 = -9 + x + 0.5x2 + 9 + -1x + -0.5x2 Combine like terms: -15 + 9 = -6 -6 + -1x + -1x + x2 + -0.5x2 = -9 + x + 0.5x2 + 9 + -1x + -0.5x2 Combine like terms: -1x + -1x = -2x -6 + -2x + x2 + -0.5x2 = -9 + x + 0.5x2 + 9 + -1x + -0.5x2 Combine like terms: x2 + -0.5x2 = 0.5x2 -6 + -2x + 0.5x2 = -9 + x + 0.5x2 + 9 + -1x + -0.5x2 Reorder the terms: -6 + -2x + 0.5x2 = -9 + 9 + x + -1x + 0.5x2 + -0.5x2 Combine like terms: -9 + 9 = 0 -6 + -2x + 0.5x2 = 0 + x + -1x + 0.5x2 + -0.5x2 -6 + -2x + 0.5x2 = x + -1x + 0.5x2 + -0.5x2 Combine like terms: x + -1x = 0 -6 + -2x + 0.5x2 = 0 + 0.5x2 + -0.5x2 -6 + -2x + 0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -6 + -2x + 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 + -4x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -4x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -4x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -4x + x2 = 0 + 12 -4x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -4x + x2 = 12 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 12 + 4 Reorder the terms: 4 + -4x + x2 = 12 + 4 Combine like terms: 12 + 4 = 16 4 + -4x + x2 = 16 Factor a perfect square on the left side: (x + -2)(x + -2) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + -2) equal to 4 and -4.Subproblem 1
x + -2 = 4 Simplifying x + -2 = 4 Reorder the terms: -2 + x = 4 Solving -2 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4 + 2 x = 4 + 2 Combine like terms: 4 + 2 = 6 x = 6 Simplifying x = 6Subproblem 2
x + -2 = -4 Simplifying x + -2 = -4 Reorder the terms: -2 + x = -4 Solving -2 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4 + 2 x = -4 + 2 Combine like terms: -4 + 2 = -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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