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Simplifying x2 + -165x + 484 = 0 Reorder the terms: 484 + -165x + x2 = 0 Solving 484 + -165x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-484' to each side of the equation. 484 + -165x + -484 + x2 = 0 + -484 Reorder the terms: 484 + -484 + -165x + x2 = 0 + -484 Combine like terms: 484 + -484 = 0 0 + -165x + x2 = 0 + -484 -165x + x2 = 0 + -484 Combine like terms: 0 + -484 = -484 -165x + x2 = -484 The x term is -165x. Take half its coefficient (-82.5). Square it (6806.25) and add it to both sides. Add '6806.25' to each side of the equation. -165x + 6806.25 + x2 = -484 + 6806.25 Reorder the terms: 6806.25 + -165x + x2 = -484 + 6806.25 Combine like terms: -484 + 6806.25 = 6322.25 6806.25 + -165x + x2 = 6322.25 Factor a perfect square on the left side: (x + -82.5)(x + -82.5) = 6322.25 Calculate the square root of the right side: 79.512577621 Break this problem into two subproblems by setting (x + -82.5) equal to 79.512577621 and -79.512577621.Subproblem 1
x + -82.5 = 79.512577621 Simplifying x + -82.5 = 79.512577621 Reorder the terms: -82.5 + x = 79.512577621 Solving -82.5 + x = 79.512577621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '82.5' to each side of the equation. -82.5 + 82.5 + x = 79.512577621 + 82.5 Combine like terms: -82.5 + 82.5 = 0.0 0.0 + x = 79.512577621 + 82.5 x = 79.512577621 + 82.5 Combine like terms: 79.512577621 + 82.5 = 162.012577621 x = 162.012577621 Simplifying x = 162.012577621Subproblem 2
x + -82.5 = -79.512577621 Simplifying x + -82.5 = -79.512577621 Reorder the terms: -82.5 + x = -79.512577621 Solving -82.5 + x = -79.512577621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '82.5' to each side of the equation. -82.5 + 82.5 + x = -79.512577621 + 82.5 Combine like terms: -82.5 + 82.5 = 0.0 0.0 + x = -79.512577621 + 82.5 x = -79.512577621 + 82.5 Combine like terms: -79.512577621 + 82.5 = 2.987422379 x = 2.987422379 Simplifying x = 2.987422379Solution
The solution to the problem is based on the solutions from the subproblems. x = {162.012577621, 2.987422379}
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