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Simplifying 2x2 + -1x + -31 = 31 Reorder the terms: -31 + -1x + 2x2 = 31 Solving -31 + -1x + 2x2 = 31 Solving for variable 'x'. Reorder the terms: -31 + -31 + -1x + 2x2 = 31 + -31 Combine like terms: -31 + -31 = -62 -62 + -1x + 2x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -62 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31 + -0.5x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + -0.5x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -0.5x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -0.5x + x2 = 0 + 31 -0.5x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -0.5x + x2 = 31 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 = 31 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 31 + 0.0625 Combine like terms: 31 + 0.0625 = 31.0625 0.0625 + -0.5x + x2 = 31.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 31.0625 Calculate the square root of the right side: 5.573374202 Break this problem into two subproblems by setting (x + -0.25) equal to 5.573374202 and -5.573374202.Subproblem 1
x + -0.25 = 5.573374202 Simplifying x + -0.25 = 5.573374202 Reorder the terms: -0.25 + x = 5.573374202 Solving -0.25 + x = 5.573374202 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 = 5.573374202 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 5.573374202 + 0.25 x = 5.573374202 + 0.25 Combine like terms: 5.573374202 + 0.25 = 5.823374202 x = 5.823374202 Simplifying x = 5.823374202Subproblem 2
x + -0.25 = -5.573374202 Simplifying x + -0.25 = -5.573374202 Reorder the terms: -0.25 + x = -5.573374202 Solving -0.25 + x = -5.573374202 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 = -5.573374202 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -5.573374202 + 0.25 x = -5.573374202 + 0.25 Combine like terms: -5.573374202 + 0.25 = -5.323374202 x = -5.323374202 Simplifying x = -5.323374202Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.823374202, -5.323374202}
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