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Simplifying x2 + 3x + -16 = 340 Reorder the terms: -16 + 3x + x2 = 340 Solving -16 + 3x + x2 = 340 Solving for variable 'x'. Reorder the terms: -16 + -340 + 3x + x2 = 340 + -340 Combine like terms: -16 + -340 = -356 -356 + 3x + x2 = 340 + -340 Combine like terms: 340 + -340 = 0 -356 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '356' to each side of the equation. -356 + 3x + 356 + x2 = 0 + 356 Reorder the terms: -356 + 356 + 3x + x2 = 0 + 356 Combine like terms: -356 + 356 = 0 0 + 3x + x2 = 0 + 356 3x + x2 = 0 + 356 Combine like terms: 0 + 356 = 356 3x + x2 = 356 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 356 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 356 + 2.25 Combine like terms: 356 + 2.25 = 358.25 2.25 + 3x + x2 = 358.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 358.25 Calculate the square root of the right side: 18.927493231 Break this problem into two subproblems by setting (x + 1.5) equal to 18.927493231 and -18.927493231.Subproblem 1
x + 1.5 = 18.927493231 Simplifying x + 1.5 = 18.927493231 Reorder the terms: 1.5 + x = 18.927493231 Solving 1.5 + x = 18.927493231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 18.927493231 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 18.927493231 + -1.5 x = 18.927493231 + -1.5 Combine like terms: 18.927493231 + -1.5 = 17.427493231 x = 17.427493231 Simplifying x = 17.427493231Subproblem 2
x + 1.5 = -18.927493231 Simplifying x + 1.5 = -18.927493231 Reorder the terms: 1.5 + x = -18.927493231 Solving 1.5 + x = -18.927493231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -18.927493231 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -18.927493231 + -1.5 x = -18.927493231 + -1.5 Combine like terms: -18.927493231 + -1.5 = -20.427493231 x = -20.427493231 Simplifying x = -20.427493231Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.427493231, -20.427493231}
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