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Simplifying 5x + 44x + x2 + -2 = 90 Reorder the terms: -2 + 5x + 44x + x2 = 90 Combine like terms: 5x + 44x = 49x -2 + 49x + x2 = 90 Solving -2 + 49x + x2 = 90 Solving for variable 'x'. Reorder the terms: -2 + -90 + 49x + x2 = 90 + -90 Combine like terms: -2 + -90 = -92 -92 + 49x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -92 + 49x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 49x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + 49x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 49x + x2 = 0 + 92 49x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 49x + x2 = 92 The x term is 49x. Take half its coefficient (24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. 49x + 600.25 + x2 = 92 + 600.25 Reorder the terms: 600.25 + 49x + x2 = 92 + 600.25 Combine like terms: 92 + 600.25 = 692.25 600.25 + 49x + x2 = 692.25 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 692.25 Calculate the square root of the right side: 26.310644234 Break this problem into two subproblems by setting (x + 24.5) equal to 26.310644234 and -26.310644234.Subproblem 1
x + 24.5 = 26.310644234 Simplifying x + 24.5 = 26.310644234 Reorder the terms: 24.5 + x = 26.310644234 Solving 24.5 + x = 26.310644234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = 26.310644234 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 26.310644234 + -24.5 x = 26.310644234 + -24.5 Combine like terms: 26.310644234 + -24.5 = 1.810644234 x = 1.810644234 Simplifying x = 1.810644234Subproblem 2
x + 24.5 = -26.310644234 Simplifying x + 24.5 = -26.310644234 Reorder the terms: 24.5 + x = -26.310644234 Solving 24.5 + x = -26.310644234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = -26.310644234 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -26.310644234 + -24.5 x = -26.310644234 + -24.5 Combine like terms: -26.310644234 + -24.5 = -50.810644234 x = -50.810644234 Simplifying x = -50.810644234Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.810644234, -50.810644234}
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