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Simplifying x2 + 47x + 48 = 0 Reorder the terms: 48 + 47x + x2 = 0 Solving 48 + 47x + 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 + 47x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + 47x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 47x + x2 = 0 + -48 47x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 47x + x2 = -48 The x term is 47x. Take half its coefficient (23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. 47x + 552.25 + x2 = -48 + 552.25 Reorder the terms: 552.25 + 47x + x2 = -48 + 552.25 Combine like terms: -48 + 552.25 = 504.25 552.25 + 47x + x2 = 504.25 Factor a perfect square on the left side: (x + 23.5)(x + 23.5) = 504.25 Calculate the square root of the right side: 22.455511573 Break this problem into two subproblems by setting (x + 23.5) equal to 22.455511573 and -22.455511573.Subproblem 1
x + 23.5 = 22.455511573 Simplifying x + 23.5 = 22.455511573 Reorder the terms: 23.5 + x = 22.455511573 Solving 23.5 + x = 22.455511573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.5' to each side of the equation. 23.5 + -23.5 + x = 22.455511573 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + x = 22.455511573 + -23.5 x = 22.455511573 + -23.5 Combine like terms: 22.455511573 + -23.5 = -1.044488427 x = -1.044488427 Simplifying x = -1.044488427Subproblem 2
x + 23.5 = -22.455511573 Simplifying x + 23.5 = -22.455511573 Reorder the terms: 23.5 + x = -22.455511573 Solving 23.5 + x = -22.455511573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.5' to each side of the equation. 23.5 + -23.5 + x = -22.455511573 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + x = -22.455511573 + -23.5 x = -22.455511573 + -23.5 Combine like terms: -22.455511573 + -23.5 = -45.955511573 x = -45.955511573 Simplifying x = -45.955511573Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.044488427, -45.955511573}
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