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Simplifying (2x2) + -1(1x) + -24 = 0 Remove parenthesis around (1x) (2x2) + -1 * 1x + -24 = 0 Multiply -1 * 1 (2x2) + -1x + -24 = 0 Reorder the terms: -24 + -1x + (2x2) = 0 Solving -24 + -1x + (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'. -12 + -0.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -0.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -0.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -0.5x + x2 = 0 + 12 -0.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -0.5x + x2 = 12 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 = 12 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 12 + 0.0625 Combine like terms: 12 + 0.0625 = 12.0625 0.0625 + -0.5x + x2 = 12.0625 Factor a perfect square on the left side: ((x) + -0.25)((x) + -0.25) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting ((x) + -0.25) equal to 3.473110997 and -3.473110997.Subproblem 1
(x) + -0.25 = 3.473110997 Simplifying (x) + -0.25 = 3.473110997 x + -0.25 = 3.473110997 Reorder the terms: -0.25 + x = 3.473110997 Solving -0.25 + x = 3.473110997 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 = 3.473110997 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.473110997 + 0.25 x = 3.473110997 + 0.25 Combine like terms: 3.473110997 + 0.25 = 3.723110997 x = 3.723110997 Simplifying x = 3.723110997Subproblem 2
(x) + -0.25 = -3.473110997 Simplifying (x) + -0.25 = -3.473110997 x + -0.25 = -3.473110997 Reorder the terms: -0.25 + x = -3.473110997 Solving -0.25 + x = -3.473110997 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 = -3.473110997 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.473110997 + 0.25 x = -3.473110997 + 0.25 Combine like terms: -3.473110997 + 0.25 = -3.223110997 x = -3.223110997 Simplifying x = -3.223110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.723110997, -3.223110997}
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