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Simplifying 22x + x2 = 520 Solving 22x + x2 = 520 Solving for variable 'x'. Reorder the terms: -520 + 22x + x2 = 520 + -520 Combine like terms: 520 + -520 = 0 -520 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '520' to each side of the equation. -520 + 22x + 520 + x2 = 0 + 520 Reorder the terms: -520 + 520 + 22x + x2 = 0 + 520 Combine like terms: -520 + 520 = 0 0 + 22x + x2 = 0 + 520 22x + x2 = 0 + 520 Combine like terms: 0 + 520 = 520 22x + x2 = 520 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 520 + 121 Reorder the terms: 121 + 22x + x2 = 520 + 121 Combine like terms: 520 + 121 = 641 121 + 22x + x2 = 641 Factor a perfect square on the left side: (x + 11)(x + 11) = 641 Calculate the square root of the right side: 25.317977802 Break this problem into two subproblems by setting (x + 11) equal to 25.317977802 and -25.317977802.Subproblem 1
x + 11 = 25.317977802 Simplifying x + 11 = 25.317977802 Reorder the terms: 11 + x = 25.317977802 Solving 11 + x = 25.317977802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 25.317977802 + -11 Combine like terms: 11 + -11 = 0 0 + x = 25.317977802 + -11 x = 25.317977802 + -11 Combine like terms: 25.317977802 + -11 = 14.317977802 x = 14.317977802 Simplifying x = 14.317977802Subproblem 2
x + 11 = -25.317977802 Simplifying x + 11 = -25.317977802 Reorder the terms: 11 + x = -25.317977802 Solving 11 + x = -25.317977802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -25.317977802 + -11 Combine like terms: 11 + -11 = 0 0 + x = -25.317977802 + -11 x = -25.317977802 + -11 Combine like terms: -25.317977802 + -11 = -36.317977802 x = -36.317977802 Simplifying x = -36.317977802Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.317977802, -36.317977802}
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