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Simplifying 30x + x2 = 54 Solving 30x + x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + 30x + x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 30x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 30x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 30x + x2 = 0 + 54 30x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 30x + x2 = 54 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 54 + 225 Reorder the terms: 225 + 30x + x2 = 54 + 225 Combine like terms: 54 + 225 = 279 225 + 30x + x2 = 279 Factor a perfect square on the left side: (x + 15)(x + 15) = 279 Calculate the square root of the right side: 16.703293088 Break this problem into two subproblems by setting (x + 15) equal to 16.703293088 and -16.703293088.Subproblem 1
x + 15 = 16.703293088 Simplifying x + 15 = 16.703293088 Reorder the terms: 15 + x = 16.703293088 Solving 15 + x = 16.703293088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 16.703293088 + -15 Combine like terms: 15 + -15 = 0 0 + x = 16.703293088 + -15 x = 16.703293088 + -15 Combine like terms: 16.703293088 + -15 = 1.703293088 x = 1.703293088 Simplifying x = 1.703293088Subproblem 2
x + 15 = -16.703293088 Simplifying x + 15 = -16.703293088 Reorder the terms: 15 + x = -16.703293088 Solving 15 + x = -16.703293088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -16.703293088 + -15 Combine like terms: 15 + -15 = 0 0 + x = -16.703293088 + -15 x = -16.703293088 + -15 Combine like terms: -16.703293088 + -15 = -31.703293088 x = -31.703293088 Simplifying x = -31.703293088Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.703293088, -31.703293088}
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