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Simplifying x2 + 10x + -48 = 0 Reorder the terms: -48 + 10x + x2 = 0 Solving -48 + 10x + 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 + 10x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 10x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 10x + x2 = 0 + 48 10x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 10x + x2 = 48 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 48 + 25 Reorder the terms: 25 + 10x + x2 = 48 + 25 Combine like terms: 48 + 25 = 73 25 + 10x + x2 = 73 Factor a perfect square on the left side: (x + 5)(x + 5) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 5) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 5 = 8.544003745 Simplifying x + 5 = 8.544003745 Reorder the terms: 5 + x = 8.544003745 Solving 5 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 8.544003745 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.544003745 + -5 x = 8.544003745 + -5 Combine like terms: 8.544003745 + -5 = 3.544003745 x = 3.544003745 Simplifying x = 3.544003745Subproblem 2
x + 5 = -8.544003745 Simplifying x + 5 = -8.544003745 Reorder the terms: 5 + x = -8.544003745 Solving 5 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -8.544003745 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.544003745 + -5 x = -8.544003745 + -5 Combine like terms: -8.544003745 + -5 = -13.544003745 x = -13.544003745 Simplifying x = -13.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.544003745, -13.544003745}
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