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Simplifying 30x + x2 + 5x = 180 Reorder the terms: 30x + 5x + x2 = 180 Combine like terms: 30x + 5x = 35x 35x + x2 = 180 Solving 35x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 35x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 35x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 35x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 35x + x2 = 0 + 180 35x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 35x + x2 = 180 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 180 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 180 + 306.25 Combine like terms: 180 + 306.25 = 486.25 306.25 + 35x + x2 = 486.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 486.25 Calculate the square root of the right side: 22.051077071 Break this problem into two subproblems by setting (x + 17.5) equal to 22.051077071 and -22.051077071.Subproblem 1
x + 17.5 = 22.051077071 Simplifying x + 17.5 = 22.051077071 Reorder the terms: 17.5 + x = 22.051077071 Solving 17.5 + x = 22.051077071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 22.051077071 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 22.051077071 + -17.5 x = 22.051077071 + -17.5 Combine like terms: 22.051077071 + -17.5 = 4.551077071 x = 4.551077071 Simplifying x = 4.551077071Subproblem 2
x + 17.5 = -22.051077071 Simplifying x + 17.5 = -22.051077071 Reorder the terms: 17.5 + x = -22.051077071 Solving 17.5 + x = -22.051077071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -22.051077071 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -22.051077071 + -17.5 x = -22.051077071 + -17.5 Combine like terms: -22.051077071 + -17.5 = -39.551077071 x = -39.551077071 Simplifying x = -39.551077071Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.551077071, -39.551077071}
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