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Simplifying 2x2 + -2x + -47 = 0 Reorder the terms: -47 + -2x + 2x2 = 0 Solving -47 + -2x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23.5 + -1x + x2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + -1x + 23.5 + x2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + -1x + x2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + -1x + x2 = 0 + 23.5 -1x + x2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 -1x + x2 = 23.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 23.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 23.5 + 0.25 Combine like terms: 23.5 + 0.25 = 23.75 0.25 + -1x + x2 = 23.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 23.75 Calculate the square root of the right side: 4.873397172 Break this problem into two subproblems by setting (x + -0.5) equal to 4.873397172 and -4.873397172.Subproblem 1
x + -0.5 = 4.873397172 Simplifying x + -0.5 = 4.873397172 Reorder the terms: -0.5 + x = 4.873397172 Solving -0.5 + x = 4.873397172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.873397172 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.873397172 + 0.5 x = 4.873397172 + 0.5 Combine like terms: 4.873397172 + 0.5 = 5.373397172 x = 5.373397172 Simplifying x = 5.373397172Subproblem 2
x + -0.5 = -4.873397172 Simplifying x + -0.5 = -4.873397172 Reorder the terms: -0.5 + x = -4.873397172 Solving -0.5 + x = -4.873397172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.873397172 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.873397172 + 0.5 x = -4.873397172 + 0.5 Combine like terms: -4.873397172 + 0.5 = -4.373397172 x = -4.373397172 Simplifying x = -4.373397172Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.373397172, -4.373397172}
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