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Simplifying x2 + 2.7x = 390 Reorder the terms: 2.7x + x2 = 390 Solving 2.7x + x2 = 390 Solving for variable 'x'. Reorder the terms: -390 + 2.7x + x2 = 390 + -390 Combine like terms: 390 + -390 = 0 -390 + 2.7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '390' to each side of the equation. -390 + 2.7x + 390 + x2 = 0 + 390 Reorder the terms: -390 + 390 + 2.7x + x2 = 0 + 390 Combine like terms: -390 + 390 = 0 0 + 2.7x + x2 = 0 + 390 2.7x + x2 = 0 + 390 Combine like terms: 0 + 390 = 390 2.7x + x2 = 390 The x term is 2.7x. Take half its coefficient (1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. 2.7x + 1.8225 + x2 = 390 + 1.8225 Reorder the terms: 1.8225 + 2.7x + x2 = 390 + 1.8225 Combine like terms: 390 + 1.8225 = 391.8225 1.8225 + 2.7x + x2 = 391.8225 Factor a perfect square on the left side: (x + 1.35)(x + 1.35) = 391.8225 Calculate the square root of the right side: 19.794506814 Break this problem into two subproblems by setting (x + 1.35) equal to 19.794506814 and -19.794506814.Subproblem 1
x + 1.35 = 19.794506814 Simplifying x + 1.35 = 19.794506814 Reorder the terms: 1.35 + x = 19.794506814 Solving 1.35 + x = 19.794506814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + x = 19.794506814 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + x = 19.794506814 + -1.35 x = 19.794506814 + -1.35 Combine like terms: 19.794506814 + -1.35 = 18.444506814 x = 18.444506814 Simplifying x = 18.444506814Subproblem 2
x + 1.35 = -19.794506814 Simplifying x + 1.35 = -19.794506814 Reorder the terms: 1.35 + x = -19.794506814 Solving 1.35 + x = -19.794506814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + x = -19.794506814 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + x = -19.794506814 + -1.35 x = -19.794506814 + -1.35 Combine like terms: -19.794506814 + -1.35 = -21.144506814 x = -21.144506814 Simplifying x = -21.144506814Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.444506814, -21.144506814}
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