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Simplifying 2x2 + -1x = 73 Reorder the terms: -1x + 2x2 = 73 Solving -1x + 2x2 = 73 Solving for variable 'x'. Reorder the terms: -73 + -1x + 2x2 = 73 + -73 Combine like terms: 73 + -73 = 0 -73 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '36.5' to each side of the equation. -36.5 + -0.5x + 36.5 + x2 = 0 + 36.5 Reorder the terms: -36.5 + 36.5 + -0.5x + x2 = 0 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + -0.5x + x2 = 0 + 36.5 -0.5x + x2 = 0 + 36.5 Combine like terms: 0 + 36.5 = 36.5 -0.5x + x2 = 36.5 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 = 36.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 36.5 + 0.0625 Combine like terms: 36.5 + 0.0625 = 36.5625 0.0625 + -0.5x + x2 = 36.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (x + -0.25) equal to 6.046693311 and -6.046693311.Subproblem 1
x + -0.25 = 6.046693311 Simplifying x + -0.25 = 6.046693311 Reorder the terms: -0.25 + x = 6.046693311 Solving -0.25 + x = 6.046693311 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 = 6.046693311 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 6.046693311 + 0.25 x = 6.046693311 + 0.25 Combine like terms: 6.046693311 + 0.25 = 6.296693311 x = 6.296693311 Simplifying x = 6.296693311Subproblem 2
x + -0.25 = -6.046693311 Simplifying x + -0.25 = -6.046693311 Reorder the terms: -0.25 + x = -6.046693311 Solving -0.25 + x = -6.046693311 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 = -6.046693311 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -6.046693311 + 0.25 x = -6.046693311 + 0.25 Combine like terms: -6.046693311 + 0.25 = -5.796693311 x = -5.796693311 Simplifying x = -5.796693311Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.296693311, -5.796693311}
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