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Simplifying (x + -19)(x + -19) = 27 Reorder the terms: (-19 + x)(x + -19) = 27 Reorder the terms: (-19 + x)(-19 + x) = 27 Multiply (-19 + x) * (-19 + x) (-19(-19 + x) + x(-19 + x)) = 27 ((-19 * -19 + x * -19) + x(-19 + x)) = 27 ((361 + -19x) + x(-19 + x)) = 27 (361 + -19x + (-19 * x + x * x)) = 27 (361 + -19x + (-19x + x2)) = 27 Combine like terms: -19x + -19x = -38x (361 + -38x + x2) = 27 Solving 361 + -38x + x2 = 27 Solving for variable 'x'. Reorder the terms: 361 + -27 + -38x + x2 = 27 + -27 Combine like terms: 361 + -27 = 334 334 + -38x + x2 = 27 + -27 Combine like terms: 27 + -27 = 0 334 + -38x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-334' to each side of the equation. 334 + -38x + -334 + x2 = 0 + -334 Reorder the terms: 334 + -334 + -38x + x2 = 0 + -334 Combine like terms: 334 + -334 = 0 0 + -38x + x2 = 0 + -334 -38x + x2 = 0 + -334 Combine like terms: 0 + -334 = -334 -38x + x2 = -334 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = -334 + 361 Reorder the terms: 361 + -38x + x2 = -334 + 361 Combine like terms: -334 + 361 = 27 361 + -38x + x2 = 27 Factor a perfect square on the left side: (x + -19)(x + -19) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -19) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -19 = 5.196152423 Simplifying x + -19 = 5.196152423 Reorder the terms: -19 + x = 5.196152423 Solving -19 + x = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 5.196152423 + 19 Combine like terms: -19 + 19 = 0 0 + x = 5.196152423 + 19 x = 5.196152423 + 19 Combine like terms: 5.196152423 + 19 = 24.196152423 x = 24.196152423 Simplifying x = 24.196152423Subproblem 2
x + -19 = -5.196152423 Simplifying x + -19 = -5.196152423 Reorder the terms: -19 + x = -5.196152423 Solving -19 + x = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -5.196152423 + 19 Combine like terms: -19 + 19 = 0 0 + x = -5.196152423 + 19 x = -5.196152423 + 19 Combine like terms: -5.196152423 + 19 = 13.803847577 x = 13.803847577 Simplifying x = 13.803847577Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.196152423, 13.803847577}
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