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Simplifying 0 = x2 + -90x + -25600 Reorder the terms: 0 = -25600 + -90x + x2 Solving 0 = -25600 + -90x + x2 Solving for variable 'x'. Combine like terms: 0 + 25600 = 25600 25600 + 90x + -1x2 = -25600 + -90x + x2 + 25600 + 90x + -1x2 Reorder the terms: 25600 + 90x + -1x2 = -25600 + 25600 + -90x + 90x + x2 + -1x2 Combine like terms: -25600 + 25600 = 0 25600 + 90x + -1x2 = 0 + -90x + 90x + x2 + -1x2 25600 + 90x + -1x2 = -90x + 90x + x2 + -1x2 Combine like terms: -90x + 90x = 0 25600 + 90x + -1x2 = 0 + x2 + -1x2 25600 + 90x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25600 + 90x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25600 + -90x + x2 = 0 Move the constant term to the right: Add '25600' to each side of the equation. -25600 + -90x + 25600 + x2 = 0 + 25600 Reorder the terms: -25600 + 25600 + -90x + x2 = 0 + 25600 Combine like terms: -25600 + 25600 = 0 0 + -90x + x2 = 0 + 25600 -90x + x2 = 0 + 25600 Combine like terms: 0 + 25600 = 25600 -90x + x2 = 25600 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = 25600 + 2025 Reorder the terms: 2025 + -90x + x2 = 25600 + 2025 Combine like terms: 25600 + 2025 = 27625 2025 + -90x + x2 = 27625 Factor a perfect square on the left side: (x + -45)(x + -45) = 27625 Calculate the square root of the right side: 166.207701386 Break this problem into two subproblems by setting (x + -45) equal to 166.207701386 and -166.207701386.Subproblem 1
x + -45 = 166.207701386 Simplifying x + -45 = 166.207701386 Reorder the terms: -45 + x = 166.207701386 Solving -45 + x = 166.207701386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 166.207701386 + 45 Combine like terms: -45 + 45 = 0 0 + x = 166.207701386 + 45 x = 166.207701386 + 45 Combine like terms: 166.207701386 + 45 = 211.207701386 x = 211.207701386 Simplifying x = 211.207701386Subproblem 2
x + -45 = -166.207701386 Simplifying x + -45 = -166.207701386 Reorder the terms: -45 + x = -166.207701386 Solving -45 + x = -166.207701386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -166.207701386 + 45 Combine like terms: -45 + 45 = 0 0 + x = -166.207701386 + 45 x = -166.207701386 + 45 Combine like terms: -166.207701386 + 45 = -121.207701386 x = -121.207701386 Simplifying x = -121.207701386Solution
The solution to the problem is based on the solutions from the subproblems. x = {211.207701386, -121.207701386}
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