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Simplifying x2 + -8x + -9 = 48 Reorder the terms: -9 + -8x + x2 = 48 Solving -9 + -8x + x2 = 48 Solving for variable 'x'. Reorder the terms: -9 + -48 + -8x + x2 = 48 + -48 Combine like terms: -9 + -48 = -57 -57 + -8x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -57 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + -8x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + -8x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + -8x + x2 = 0 + 57 -8x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 -8x + x2 = 57 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 57 + 16 Reorder the terms: 16 + -8x + x2 = 57 + 16 Combine like terms: 57 + 16 = 73 16 + -8x + x2 = 73 Factor a perfect square on the left side: (x + -4)(x + -4) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -4) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -4 = 8.544003745 Simplifying x + -4 = 8.544003745 Reorder the terms: -4 + x = 8.544003745 Solving -4 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.544003745 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.544003745 + 4 x = 8.544003745 + 4 Combine like terms: 8.544003745 + 4 = 12.544003745 x = 12.544003745 Simplifying x = 12.544003745Subproblem 2
x + -4 = -8.544003745 Simplifying x + -4 = -8.544003745 Reorder the terms: -4 + x = -8.544003745 Solving -4 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.544003745 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.544003745 + 4 x = -8.544003745 + 4 Combine like terms: -8.544003745 + 4 = -4.544003745 x = -4.544003745 Simplifying x = -4.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.544003745, -4.544003745}
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