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Simplifying 0 = x2 + -36x + 191 Reorder the terms: 0 = 191 + -36x + x2 Solving 0 = 191 + -36x + x2 Solving for variable 'x'. Combine like terms: 0 + -191 = -191 -191 + 36x + -1x2 = 191 + -36x + x2 + -191 + 36x + -1x2 Reorder the terms: -191 + 36x + -1x2 = 191 + -191 + -36x + 36x + x2 + -1x2 Combine like terms: 191 + -191 = 0 -191 + 36x + -1x2 = 0 + -36x + 36x + x2 + -1x2 -191 + 36x + -1x2 = -36x + 36x + x2 + -1x2 Combine like terms: -36x + 36x = 0 -191 + 36x + -1x2 = 0 + x2 + -1x2 -191 + 36x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -191 + 36x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 191 + -36x + x2 = 0 Move the constant term to the right: Add '-191' to each side of the equation. 191 + -36x + -191 + x2 = 0 + -191 Reorder the terms: 191 + -191 + -36x + x2 = 0 + -191 Combine like terms: 191 + -191 = 0 0 + -36x + x2 = 0 + -191 -36x + x2 = 0 + -191 Combine like terms: 0 + -191 = -191 -36x + x2 = -191 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = -191 + 324 Reorder the terms: 324 + -36x + x2 = -191 + 324 Combine like terms: -191 + 324 = 133 324 + -36x + x2 = 133 Factor a perfect square on the left side: (x + -18)(x + -18) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + -18) equal to 11.532562595 and -11.532562595.Subproblem 1
x + -18 = 11.532562595 Simplifying x + -18 = 11.532562595 Reorder the terms: -18 + x = 11.532562595 Solving -18 + x = 11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 11.532562595 + 18 Combine like terms: -18 + 18 = 0 0 + x = 11.532562595 + 18 x = 11.532562595 + 18 Combine like terms: 11.532562595 + 18 = 29.532562595 x = 29.532562595 Simplifying x = 29.532562595Subproblem 2
x + -18 = -11.532562595 Simplifying x + -18 = -11.532562595 Reorder the terms: -18 + x = -11.532562595 Solving -18 + x = -11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -11.532562595 + 18 Combine like terms: -18 + 18 = 0 0 + x = -11.532562595 + 18 x = -11.532562595 + 18 Combine like terms: -11.532562595 + 18 = 6.467437405 x = 6.467437405 Simplifying x = 6.467437405Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.532562595, 6.467437405}
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