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Simplifying 2x2 + -1x + 0.25 = 6 Reorder the terms: 0.25 + -1x + 2x2 = 6 Solving 0.25 + -1x + 2x2 = 6 Solving for variable 'x'. Reorder the terms: 0.25 + -6 + -1x + 2x2 = 6 + -6 Combine like terms: 0.25 + -6 = -5.75 -5.75 + -1x + 2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -5.75 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.875 + -0.5x + x2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + -0.5x + 2.875 + x2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + -0.5x + x2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + -0.5x + x2 = 0 + 2.875 -0.5x + x2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 -0.5x + x2 = 2.875 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 = 2.875 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 2.875 + 0.0625 Combine like terms: 2.875 + 0.0625 = 2.9375 0.0625 + -0.5x + x2 = 2.9375 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 2.9375 Calculate the square root of the right side: 1.71391365 Break this problem into two subproblems by setting (x + -0.25) equal to 1.71391365 and -1.71391365.Subproblem 1
x + -0.25 = 1.71391365 Simplifying x + -0.25 = 1.71391365 Reorder the terms: -0.25 + x = 1.71391365 Solving -0.25 + x = 1.71391365 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 = 1.71391365 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.71391365 + 0.25 x = 1.71391365 + 0.25 Combine like terms: 1.71391365 + 0.25 = 1.96391365 x = 1.96391365 Simplifying x = 1.96391365Subproblem 2
x + -0.25 = -1.71391365 Simplifying x + -0.25 = -1.71391365 Reorder the terms: -0.25 + x = -1.71391365 Solving -0.25 + x = -1.71391365 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 = -1.71391365 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.71391365 + 0.25 x = -1.71391365 + 0.25 Combine like terms: -1.71391365 + 0.25 = -1.46391365 x = -1.46391365 Simplifying x = -1.46391365Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.96391365, -1.46391365}
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