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Simplifying 230 = 90x + -1x2 Solving 230 = 90x + -1x2 Solving for variable 'x'. Reorder the terms: 230 + -90x + x2 = 90x + -90x + -1x2 + x2 Combine like terms: 90x + -90x = 0 230 + -90x + x2 = 0 + -1x2 + x2 230 + -90x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 230 + -90x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-230' to each side of the equation. 230 + -90x + -230 + x2 = 0 + -230 Reorder the terms: 230 + -230 + -90x + x2 = 0 + -230 Combine like terms: 230 + -230 = 0 0 + -90x + x2 = 0 + -230 -90x + x2 = 0 + -230 Combine like terms: 0 + -230 = -230 -90x + x2 = -230 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 = -230 + 2025 Reorder the terms: 2025 + -90x + x2 = -230 + 2025 Combine like terms: -230 + 2025 = 1795 2025 + -90x + x2 = 1795 Factor a perfect square on the left side: (x + -45)(x + -45) = 1795 Calculate the square root of the right side: 42.367440329 Break this problem into two subproblems by setting (x + -45) equal to 42.367440329 and -42.367440329.Subproblem 1
x + -45 = 42.367440329 Simplifying x + -45 = 42.367440329 Reorder the terms: -45 + x = 42.367440329 Solving -45 + x = 42.367440329 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 = 42.367440329 + 45 Combine like terms: -45 + 45 = 0 0 + x = 42.367440329 + 45 x = 42.367440329 + 45 Combine like terms: 42.367440329 + 45 = 87.367440329 x = 87.367440329 Simplifying x = 87.367440329Subproblem 2
x + -45 = -42.367440329 Simplifying x + -45 = -42.367440329 Reorder the terms: -45 + x = -42.367440329 Solving -45 + x = -42.367440329 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 = -42.367440329 + 45 Combine like terms: -45 + 45 = 0 0 + x = -42.367440329 + 45 x = -42.367440329 + 45 Combine like terms: -42.367440329 + 45 = 2.632559671 x = 2.632559671 Simplifying x = 2.632559671Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.367440329, 2.632559671}
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