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Simplifying x2 + 4.6x = 319 Reorder the terms: 4.6x + x2 = 319 Solving 4.6x + x2 = 319 Solving for variable 'x'. Reorder the terms: -319 + 4.6x + x2 = 319 + -319 Combine like terms: 319 + -319 = 0 -319 + 4.6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '319' to each side of the equation. -319 + 4.6x + 319 + x2 = 0 + 319 Reorder the terms: -319 + 319 + 4.6x + x2 = 0 + 319 Combine like terms: -319 + 319 = 0 0 + 4.6x + x2 = 0 + 319 4.6x + x2 = 0 + 319 Combine like terms: 0 + 319 = 319 4.6x + x2 = 319 The x term is 4.6x. Take half its coefficient (2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. 4.6x + 5.29 + x2 = 319 + 5.29 Reorder the terms: 5.29 + 4.6x + x2 = 319 + 5.29 Combine like terms: 319 + 5.29 = 324.29 5.29 + 4.6x + x2 = 324.29 Factor a perfect square on the left side: (x + 2.3)(x + 2.3) = 324.29 Calculate the square root of the right side: 18.008053754 Break this problem into two subproblems by setting (x + 2.3) equal to 18.008053754 and -18.008053754.Subproblem 1
x + 2.3 = 18.008053754 Simplifying x + 2.3 = 18.008053754 Reorder the terms: 2.3 + x = 18.008053754 Solving 2.3 + x = 18.008053754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = 18.008053754 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = 18.008053754 + -2.3 x = 18.008053754 + -2.3 Combine like terms: 18.008053754 + -2.3 = 15.708053754 x = 15.708053754 Simplifying x = 15.708053754Subproblem 2
x + 2.3 = -18.008053754 Simplifying x + 2.3 = -18.008053754 Reorder the terms: 2.3 + x = -18.008053754 Solving 2.3 + x = -18.008053754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = -18.008053754 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = -18.008053754 + -2.3 x = -18.008053754 + -2.3 Combine like terms: -18.008053754 + -2.3 = -20.308053754 x = -20.308053754 Simplifying x = -20.308053754Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.708053754, -20.308053754}
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