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Simplifying 2x2 + -1x = 224 Reorder the terms: -1x + 2x2 = 224 Solving -1x + 2x2 = 224 Solving for variable 'x'. Reorder the terms: -224 + -1x + 2x2 = 224 + -224 Combine like terms: 224 + -224 = 0 -224 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -112 + -0.5x + x2 = 0 Move the constant term to the right: Add '112' to each side of the equation. -112 + -0.5x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + -0.5x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -0.5x + x2 = 0 + 112 -0.5x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 -0.5x + x2 = 112 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 = 112 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 112 + 0.0625 Combine like terms: 112 + 0.0625 = 112.0625 0.0625 + -0.5x + x2 = 112.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 112.0625 Calculate the square root of the right side: 10.58595768 Break this problem into two subproblems by setting (x + -0.25) equal to 10.58595768 and -10.58595768.Subproblem 1
x + -0.25 = 10.58595768 Simplifying x + -0.25 = 10.58595768 Reorder the terms: -0.25 + x = 10.58595768 Solving -0.25 + x = 10.58595768 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 = 10.58595768 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 10.58595768 + 0.25 x = 10.58595768 + 0.25 Combine like terms: 10.58595768 + 0.25 = 10.83595768 x = 10.83595768 Simplifying x = 10.83595768Subproblem 2
x + -0.25 = -10.58595768 Simplifying x + -0.25 = -10.58595768 Reorder the terms: -0.25 + x = -10.58595768 Solving -0.25 + x = -10.58595768 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 = -10.58595768 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -10.58595768 + 0.25 x = -10.58595768 + 0.25 Combine like terms: -10.58595768 + 0.25 = -10.33595768 x = -10.33595768 Simplifying x = -10.33595768Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.83595768, -10.33595768}
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