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Simplifying 0 = x2 + 90x + 38 Reorder the terms: 0 = 38 + 90x + x2 Solving 0 = 38 + 90x + x2 Solving for variable 'x'. Combine like terms: 0 + -38 = -38 -38 + -90x + -1x2 = 38 + 90x + x2 + -38 + -90x + -1x2 Reorder the terms: -38 + -90x + -1x2 = 38 + -38 + 90x + -90x + x2 + -1x2 Combine like terms: 38 + -38 = 0 -38 + -90x + -1x2 = 0 + 90x + -90x + x2 + -1x2 -38 + -90x + -1x2 = 90x + -90x + x2 + -1x2 Combine like terms: 90x + -90x = 0 -38 + -90x + -1x2 = 0 + x2 + -1x2 -38 + -90x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -38 + -90x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(38 + 90x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(38 + 90x + x2)' equal to zero and attempt to solve: Simplifying 38 + 90x + x2 = 0 Solving 38 + 90x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + 90x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + 90x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 90x + x2 = 0 + -38 90x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 90x + x2 = -38 The x term is 90x. Take half its coefficient (45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. 90x + 2025 + x2 = -38 + 2025 Reorder the terms: 2025 + 90x + x2 = -38 + 2025 Combine like terms: -38 + 2025 = 1987 2025 + 90x + x2 = 1987 Factor a perfect square on the left side: (x + 45)(x + 45) = 1987 Calculate the square root of the right side: 44.575778176 Break this problem into two subproblems by setting (x + 45) equal to 44.575778176 and -44.575778176.Subproblem 1
x + 45 = 44.575778176 Simplifying x + 45 = 44.575778176 Reorder the terms: 45 + x = 44.575778176 Solving 45 + x = 44.575778176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 44.575778176 + -45 Combine like terms: 45 + -45 = 0 0 + x = 44.575778176 + -45 x = 44.575778176 + -45 Combine like terms: 44.575778176 + -45 = -0.424221824 x = -0.424221824 Simplifying x = -0.424221824Subproblem 2
x + 45 = -44.575778176 Simplifying x + 45 = -44.575778176 Reorder the terms: 45 + x = -44.575778176 Solving 45 + x = -44.575778176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = -44.575778176 + -45 Combine like terms: 45 + -45 = 0 0 + x = -44.575778176 + -45 x = -44.575778176 + -45 Combine like terms: -44.575778176 + -45 = -89.575778176 x = -89.575778176 Simplifying x = -89.575778176Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.424221824, -89.575778176}Solution
x = {-0.424221824, -89.575778176}
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