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Simplifying x2 = (25 + -1x)(3x + 55) Reorder the terms: x2 = (25 + -1x)(55 + 3x) Multiply (25 + -1x) * (55 + 3x) x2 = (25(55 + 3x) + -1x * (55 + 3x)) x2 = ((55 * 25 + 3x * 25) + -1x * (55 + 3x)) x2 = ((1375 + 75x) + -1x * (55 + 3x)) x2 = (1375 + 75x + (55 * -1x + 3x * -1x)) x2 = (1375 + 75x + (-55x + -3x2)) Combine like terms: 75x + -55x = 20x x2 = (1375 + 20x + -3x2) Solving x2 = 1375 + 20x + -3x2 Solving for variable 'x'. Reorder the terms: -1375 + -20x + x2 + 3x2 = 1375 + 20x + -3x2 + -1375 + -20x + 3x2 Combine like terms: x2 + 3x2 = 4x2 -1375 + -20x + 4x2 = 1375 + 20x + -3x2 + -1375 + -20x + 3x2 Reorder the terms: -1375 + -20x + 4x2 = 1375 + -1375 + 20x + -20x + -3x2 + 3x2 Combine like terms: 1375 + -1375 = 0 -1375 + -20x + 4x2 = 0 + 20x + -20x + -3x2 + 3x2 -1375 + -20x + 4x2 = 20x + -20x + -3x2 + 3x2 Combine like terms: 20x + -20x = 0 -1375 + -20x + 4x2 = 0 + -3x2 + 3x2 -1375 + -20x + 4x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -1375 + -20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -343.75 + -5x + x2 = 0 Move the constant term to the right: Add '343.75' to each side of the equation. -343.75 + -5x + 343.75 + x2 = 0 + 343.75 Reorder the terms: -343.75 + 343.75 + -5x + x2 = 0 + 343.75 Combine like terms: -343.75 + 343.75 = 0.00 0.00 + -5x + x2 = 0 + 343.75 -5x + x2 = 0 + 343.75 Combine like terms: 0 + 343.75 = 343.75 -5x + x2 = 343.75 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 343.75 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 343.75 + 6.25 Combine like terms: 343.75 + 6.25 = 350 6.25 + -5x + x2 = 350 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 350 Calculate the square root of the right side: 18.708286934 Break this problem into two subproblems by setting (x + -2.5) equal to 18.708286934 and -18.708286934.Subproblem 1
x + -2.5 = 18.708286934 Simplifying x + -2.5 = 18.708286934 Reorder the terms: -2.5 + x = 18.708286934 Solving -2.5 + x = 18.708286934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 18.708286934 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 18.708286934 + 2.5 x = 18.708286934 + 2.5 Combine like terms: 18.708286934 + 2.5 = 21.208286934 x = 21.208286934 Simplifying x = 21.208286934Subproblem 2
x + -2.5 = -18.708286934 Simplifying x + -2.5 = -18.708286934 Reorder the terms: -2.5 + x = -18.708286934 Solving -2.5 + x = -18.708286934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -18.708286934 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -18.708286934 + 2.5 x = -18.708286934 + 2.5 Combine like terms: -18.708286934 + 2.5 = -16.208286934 x = -16.208286934 Simplifying x = -16.208286934Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.208286934, -16.208286934}
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