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Simplifying x2 + -23x + -48 = 0 Reorder the terms: -48 + -23x + x2 = 0 Solving -48 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -23x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -23x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -23x + x2 = 0 + 48 -23x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -23x + x2 = 48 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = 48 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 48 + 132.25 Combine like terms: 48 + 132.25 = 180.25 132.25 + -23x + x2 = 180.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + -11.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + -11.5 = 13.425721582 Simplifying x + -11.5 = 13.425721582 Reorder the terms: -11.5 + x = 13.425721582 Solving -11.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 13.425721582 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 13.425721582 + 11.5 x = 13.425721582 + 11.5 Combine like terms: 13.425721582 + 11.5 = 24.925721582 x = 24.925721582 Simplifying x = 24.925721582Subproblem 2
x + -11.5 = -13.425721582 Simplifying x + -11.5 = -13.425721582 Reorder the terms: -11.5 + x = -13.425721582 Solving -11.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -13.425721582 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -13.425721582 + 11.5 x = -13.425721582 + 11.5 Combine like terms: -13.425721582 + 11.5 = -1.925721582 x = -1.925721582 Simplifying x = -1.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.925721582, -1.925721582}
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