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Simplifying x2 + 19x + 73 = 28 Reorder the terms: 73 + 19x + x2 = 28 Solving 73 + 19x + x2 = 28 Solving for variable 'x'. Reorder the terms: 73 + -28 + 19x + x2 = 28 + -28 Combine like terms: 73 + -28 = 45 45 + 19x + x2 = 28 + -28 Combine like terms: 28 + -28 = 0 45 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 19x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + 19x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 19x + x2 = 0 + -45 19x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 19x + x2 = -45 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -45 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -45 + 90.25 Combine like terms: -45 + 90.25 = 45.25 90.25 + 19x + x2 = 45.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + 9.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + 9.5 = 6.726812024 Simplifying x + 9.5 = 6.726812024 Reorder the terms: 9.5 + x = 6.726812024 Solving 9.5 + x = 6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 6.726812024 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 6.726812024 + -9.5 x = 6.726812024 + -9.5 Combine like terms: 6.726812024 + -9.5 = -2.773187976 x = -2.773187976 Simplifying x = -2.773187976Subproblem 2
x + 9.5 = -6.726812024 Simplifying x + 9.5 = -6.726812024 Reorder the terms: 9.5 + x = -6.726812024 Solving 9.5 + x = -6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -6.726812024 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -6.726812024 + -9.5 x = -6.726812024 + -9.5 Combine like terms: -6.726812024 + -9.5 = -16.226812024 x = -16.226812024 Simplifying x = -16.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.773187976, -16.226812024}
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