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Simplifying (2x2) + -1(7x) + -18x = 5 Remove parenthesis around (7x) (2x2) + -1 * 7x + -18x = 5 Multiply -1 * 7 (2x2) + -7x + -18x = 5 Reorder the terms: -7x + -18x + (2x2) = 5 Combine like terms: -7x + -18x = -25x -25x + (2x2) = 5 Solving -25x + (2x2) = 5 Solving for variable 'x'. Reorder the terms: -5 + -25x + (2x2) = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -25x + (2x2) = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -12.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -12.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -12.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -12.5x + x2 = 0 + 2.5 -12.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -12.5x + x2 = 2.5 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 2.5 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 2.5 + 39.0625 Combine like terms: 2.5 + 39.0625 = 41.5625 39.0625 + -12.5x + x2 = 41.5625 Factor a perfect square on the left side: ((x) + -6.25)((x) + -6.25) = 41.5625 Calculate the square root of the right side: 6.446898479 Break this problem into two subproblems by setting ((x) + -6.25) equal to 6.446898479 and -6.446898479.Subproblem 1
(x) + -6.25 = 6.446898479 Simplifying (x) + -6.25 = 6.446898479 x + -6.25 = 6.446898479 Reorder the terms: -6.25 + x = 6.446898479 Solving -6.25 + x = 6.446898479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 6.446898479 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 6.446898479 + 6.25 x = 6.446898479 + 6.25 Combine like terms: 6.446898479 + 6.25 = 12.696898479 x = 12.696898479 Simplifying x = 12.696898479Subproblem 2
(x) + -6.25 = -6.446898479 Simplifying (x) + -6.25 = -6.446898479 x + -6.25 = -6.446898479 Reorder the terms: -6.25 + x = -6.446898479 Solving -6.25 + x = -6.446898479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -6.446898479 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -6.446898479 + 6.25 x = -6.446898479 + 6.25 Combine like terms: -6.446898479 + 6.25 = -0.196898479 x = -0.196898479 Simplifying x = -0.196898479Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.696898479, -0.196898479}
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