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Simplifying 2x2 + -1x + -3 = 294 Reorder the terms: -3 + -1x + 2x2 = 294 Solving -3 + -1x + 2x2 = 294 Solving for variable 'x'. Reorder the terms: -3 + -294 + -1x + 2x2 = 294 + -294 Combine like terms: -3 + -294 = -297 -297 + -1x + 2x2 = 294 + -294 Combine like terms: 294 + -294 = 0 -297 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -148.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '148.5' to each side of the equation. -148.5 + -0.5x + 148.5 + x2 = 0 + 148.5 Reorder the terms: -148.5 + 148.5 + -0.5x + x2 = 0 + 148.5 Combine like terms: -148.5 + 148.5 = 0.0 0.0 + -0.5x + x2 = 0 + 148.5 -0.5x + x2 = 0 + 148.5 Combine like terms: 0 + 148.5 = 148.5 -0.5x + x2 = 148.5 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 = 148.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 148.5 + 0.0625 Combine like terms: 148.5 + 0.0625 = 148.5625 0.0625 + -0.5x + x2 = 148.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 148.5625 Calculate the square root of the right side: 12.188621743 Break this problem into two subproblems by setting (x + -0.25) equal to 12.188621743 and -12.188621743.Subproblem 1
x + -0.25 = 12.188621743 Simplifying x + -0.25 = 12.188621743 Reorder the terms: -0.25 + x = 12.188621743 Solving -0.25 + x = 12.188621743 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 = 12.188621743 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 12.188621743 + 0.25 x = 12.188621743 + 0.25 Combine like terms: 12.188621743 + 0.25 = 12.438621743 x = 12.438621743 Simplifying x = 12.438621743Subproblem 2
x + -0.25 = -12.188621743 Simplifying x + -0.25 = -12.188621743 Reorder the terms: -0.25 + x = -12.188621743 Solving -0.25 + x = -12.188621743 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 = -12.188621743 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -12.188621743 + 0.25 x = -12.188621743 + 0.25 Combine like terms: -12.188621743 + 0.25 = -11.938621743 x = -11.938621743 Simplifying x = -11.938621743Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.438621743, -11.938621743}
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