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Simplifying 2x2 = x + 150 Reorder the terms: 2x2 = 150 + x Solving 2x2 = 150 + x Solving for variable 'x'. Reorder the terms: -150 + -1x + 2x2 = 150 + x + -150 + -1x Reorder the terms: -150 + -1x + 2x2 = 150 + -150 + x + -1x Combine like terms: 150 + -150 = 0 -150 + -1x + 2x2 = 0 + x + -1x -150 + -1x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -150 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -75 + -0.5x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + -0.5x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -0.5x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -0.5x + x2 = 0 + 75 -0.5x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -0.5x + x2 = 75 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 75 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 75 + 0.0625 Combine like terms: 75 + 0.0625 = 75.0625 0.0625 + -0.5x + x2 = 75.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 75.0625 Calculate the square root of the right side: 8.663861726 Break this problem into two subproblems by setting (x + -0.25) equal to 8.663861726 and -8.663861726.Subproblem 1
x + -0.25 = 8.663861726 Simplifying x + -0.25 = 8.663861726 Reorder the terms: -0.25 + x = 8.663861726 Solving -0.25 + x = 8.663861726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 8.663861726 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 8.663861726 + 0.25 x = 8.663861726 + 0.25 Combine like terms: 8.663861726 + 0.25 = 8.913861726 x = 8.913861726 Simplifying x = 8.913861726Subproblem 2
x + -0.25 = -8.663861726 Simplifying x + -0.25 = -8.663861726 Reorder the terms: -0.25 + x = -8.663861726 Solving -0.25 + x = -8.663861726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -8.663861726 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -8.663861726 + 0.25 x = -8.663861726 + 0.25 Combine like terms: -8.663861726 + 0.25 = -8.413861726 x = -8.413861726 Simplifying x = -8.413861726Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.913861726, -8.413861726}
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