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Simplifying x2 + 19x + -90 = 0 Reorder the terms: -90 + 19x + x2 = 0 Solving -90 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 19x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 19x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 19x + x2 = 0 + 90 19x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 19x + x2 = 90 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 = 90 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 90 + 90.25 Combine like terms: 90 + 90.25 = 180.25 90.25 + 19x + x2 = 180.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + 9.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + 9.5 = 13.425721582 Simplifying x + 9.5 = 13.425721582 Reorder the terms: 9.5 + x = 13.425721582 Solving 9.5 + x = 13.425721582 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 = 13.425721582 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 13.425721582 + -9.5 x = 13.425721582 + -9.5 Combine like terms: 13.425721582 + -9.5 = 3.925721582 x = 3.925721582 Simplifying x = 3.925721582Subproblem 2
x + 9.5 = -13.425721582 Simplifying x + 9.5 = -13.425721582 Reorder the terms: 9.5 + x = -13.425721582 Solving 9.5 + x = -13.425721582 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 = -13.425721582 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -13.425721582 + -9.5 x = -13.425721582 + -9.5 Combine like terms: -13.425721582 + -9.5 = -22.925721582 x = -22.925721582 Simplifying x = -22.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.925721582, -22.925721582}
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