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Simplifying 5 = x2 + -12x + -32 Reorder the terms: 5 = -32 + -12x + x2 Solving 5 = -32 + -12x + x2 Solving for variable 'x'. Combine like terms: 5 + 32 = 37 37 + 12x + -1x2 = -32 + -12x + x2 + 32 + 12x + -1x2 Reorder the terms: 37 + 12x + -1x2 = -32 + 32 + -12x + 12x + x2 + -1x2 Combine like terms: -32 + 32 = 0 37 + 12x + -1x2 = 0 + -12x + 12x + x2 + -1x2 37 + 12x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 37 + 12x + -1x2 = 0 + x2 + -1x2 37 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 37 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -37 + -12x + x2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + -12x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + -12x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -12x + x2 = 0 + 37 -12x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 -12x + x2 = 37 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 37 + 36 Reorder the terms: 36 + -12x + x2 = 37 + 36 Combine like terms: 37 + 36 = 73 36 + -12x + x2 = 73 Factor a perfect square on the left side: (x + -6)(x + -6) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -6) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -6 = 8.544003745 Simplifying x + -6 = 8.544003745 Reorder the terms: -6 + x = 8.544003745 Solving -6 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.544003745 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.544003745 + 6 x = 8.544003745 + 6 Combine like terms: 8.544003745 + 6 = 14.544003745 x = 14.544003745 Simplifying x = 14.544003745Subproblem 2
x + -6 = -8.544003745 Simplifying x + -6 = -8.544003745 Reorder the terms: -6 + x = -8.544003745 Solving -6 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.544003745 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.544003745 + 6 x = -8.544003745 + 6 Combine like terms: -8.544003745 + 6 = -2.544003745 x = -2.544003745 Simplifying x = -2.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.544003745, -2.544003745}
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