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Simplifying x2 + 25 + 9x + 5 = 180 Reorder the terms: 25 + 5 + 9x + x2 = 180 Combine like terms: 25 + 5 = 30 30 + 9x + x2 = 180 Solving 30 + 9x + x2 = 180 Solving for variable 'x'. Reorder the terms: 30 + -180 + 9x + x2 = 180 + -180 Combine like terms: 30 + -180 = -150 -150 + 9x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -150 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 9x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 9x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 9x + x2 = 0 + 150 9x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 9x + x2 = 150 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 150 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 150 + 20.25 Combine like terms: 150 + 20.25 = 170.25 20.25 + 9x + x2 = 170.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 170.25 Calculate the square root of the right side: 13.047988351 Break this problem into two subproblems by setting (x + 4.5) equal to 13.047988351 and -13.047988351.Subproblem 1
x + 4.5 = 13.047988351 Simplifying x + 4.5 = 13.047988351 Reorder the terms: 4.5 + x = 13.047988351 Solving 4.5 + x = 13.047988351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 13.047988351 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 13.047988351 + -4.5 x = 13.047988351 + -4.5 Combine like terms: 13.047988351 + -4.5 = 8.547988351 x = 8.547988351 Simplifying x = 8.547988351Subproblem 2
x + 4.5 = -13.047988351 Simplifying x + 4.5 = -13.047988351 Reorder the terms: 4.5 + x = -13.047988351 Solving 4.5 + x = -13.047988351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -13.047988351 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -13.047988351 + -4.5 x = -13.047988351 + -4.5 Combine like terms: -13.047988351 + -4.5 = -17.547988351 x = -17.547988351 Simplifying x = -17.547988351Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.547988351, -17.547988351}
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