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Simplifying x = (60 + -2x)(45 + -2x) Multiply (60 + -2x) * (45 + -2x) x = (60(45 + -2x) + -2x * (45 + -2x)) x = ((45 * 60 + -2x * 60) + -2x * (45 + -2x)) x = ((2700 + -120x) + -2x * (45 + -2x)) x = (2700 + -120x + (45 * -2x + -2x * -2x)) x = (2700 + -120x + (-90x + 4x2)) Combine like terms: -120x + -90x = -210x x = (2700 + -210x + 4x2) Solving x = 2700 + -210x + 4x2 Solving for variable 'x'. Reorder the terms: -2700 + x + 210x + -4x2 = 2700 + -210x + 4x2 + -2700 + 210x + -4x2 Combine like terms: x + 210x = 211x -2700 + 211x + -4x2 = 2700 + -210x + 4x2 + -2700 + 210x + -4x2 Reorder the terms: -2700 + 211x + -4x2 = 2700 + -2700 + -210x + 210x + 4x2 + -4x2 Combine like terms: 2700 + -2700 = 0 -2700 + 211x + -4x2 = 0 + -210x + 210x + 4x2 + -4x2 -2700 + 211x + -4x2 = -210x + 210x + 4x2 + -4x2 Combine like terms: -210x + 210x = 0 -2700 + 211x + -4x2 = 0 + 4x2 + -4x2 -2700 + 211x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -2700 + 211x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 675 + -52.75x + x2 = 0 Move the constant term to the right: Add '-675' to each side of the equation. 675 + -52.75x + -675 + x2 = 0 + -675 Reorder the terms: 675 + -675 + -52.75x + x2 = 0 + -675 Combine like terms: 675 + -675 = 0 0 + -52.75x + x2 = 0 + -675 -52.75x + x2 = 0 + -675 Combine like terms: 0 + -675 = -675 -52.75x + x2 = -675 The x term is -52.75x. Take half its coefficient (-26.375). Square it (695.640625) and add it to both sides. Add '695.640625' to each side of the equation. -52.75x + 695.640625 + x2 = -675 + 695.640625 Reorder the terms: 695.640625 + -52.75x + x2 = -675 + 695.640625 Combine like terms: -675 + 695.640625 = 20.640625 695.640625 + -52.75x + x2 = 20.640625 Factor a perfect square on the left side: (x + -26.375)(x + -26.375) = 20.640625 Calculate the square root of the right side: 4.543195461 Break this problem into two subproblems by setting (x + -26.375) equal to 4.543195461 and -4.543195461.Subproblem 1
x + -26.375 = 4.543195461 Simplifying x + -26.375 = 4.543195461 Reorder the terms: -26.375 + x = 4.543195461 Solving -26.375 + x = 4.543195461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.375' to each side of the equation. -26.375 + 26.375 + x = 4.543195461 + 26.375 Combine like terms: -26.375 + 26.375 = 0.000 0.000 + x = 4.543195461 + 26.375 x = 4.543195461 + 26.375 Combine like terms: 4.543195461 + 26.375 = 30.918195461 x = 30.918195461 Simplifying x = 30.918195461Subproblem 2
x + -26.375 = -4.543195461 Simplifying x + -26.375 = -4.543195461 Reorder the terms: -26.375 + x = -4.543195461 Solving -26.375 + x = -4.543195461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.375' to each side of the equation. -26.375 + 26.375 + x = -4.543195461 + 26.375 Combine like terms: -26.375 + 26.375 = 0.000 0.000 + x = -4.543195461 + 26.375 x = -4.543195461 + 26.375 Combine like terms: -4.543195461 + 26.375 = 21.831804539 x = 21.831804539 Simplifying x = 21.831804539Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.918195461, 21.831804539}
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