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Simplifying 0.5 = -1x2 + x + 12 Reorder the terms: 0.5 = 12 + x + -1x2 Solving 0.5 = 12 + x + -1x2 Solving for variable 'x'. Combine like terms: 0.5 + -12 = -11.5 -11.5 + -1x + x2 = 12 + x + -1x2 + -12 + -1x + x2 Reorder the terms: -11.5 + -1x + x2 = 12 + -12 + x + -1x + -1x2 + x2 Combine like terms: 12 + -12 = 0 -11.5 + -1x + x2 = 0 + x + -1x + -1x2 + x2 -11.5 + -1x + x2 = x + -1x + -1x2 + x2 Combine like terms: x + -1x = 0 -11.5 + -1x + x2 = 0 + -1x2 + x2 -11.5 + -1x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -11.5 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -1x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -1x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -1x + x2 = 0 + 11.5 -1x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -1x + x2 = 11.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 11.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 11.5 + 0.25 Combine like terms: 11.5 + 0.25 = 11.75 0.25 + -1x + x2 = 11.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (x + -0.5) equal to 3.4278273 and -3.4278273.Subproblem 1
x + -0.5 = 3.4278273 Simplifying x + -0.5 = 3.4278273 Reorder the terms: -0.5 + x = 3.4278273 Solving -0.5 + x = 3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.4278273 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.4278273 + 0.5 x = 3.4278273 + 0.5 Combine like terms: 3.4278273 + 0.5 = 3.9278273 x = 3.9278273 Simplifying x = 3.9278273Subproblem 2
x + -0.5 = -3.4278273 Simplifying x + -0.5 = -3.4278273 Reorder the terms: -0.5 + x = -3.4278273 Solving -0.5 + x = -3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.4278273 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.4278273 + 0.5 x = -3.4278273 + 0.5 Combine like terms: -3.4278273 + 0.5 = -2.9278273 x = -2.9278273 Simplifying x = -2.9278273Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9278273, -2.9278273}
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