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Simplifying x2 + -26x + 36 = 0 Reorder the terms: 36 + -26x + x2 = 0 Solving 36 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -26x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -26x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -26x + x2 = 0 + -36 -26x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -26x + x2 = -36 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -36 + 169 Reorder the terms: 169 + -26x + x2 = -36 + 169 Combine like terms: -36 + 169 = 133 169 + -26x + x2 = 133 Factor a perfect square on the left side: (x + -13)(x + -13) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + -13) equal to 11.532562595 and -11.532562595.Subproblem 1
x + -13 = 11.532562595 Simplifying x + -13 = 11.532562595 Reorder the terms: -13 + x = 11.532562595 Solving -13 + x = 11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 11.532562595 + 13 Combine like terms: -13 + 13 = 0 0 + x = 11.532562595 + 13 x = 11.532562595 + 13 Combine like terms: 11.532562595 + 13 = 24.532562595 x = 24.532562595 Simplifying x = 24.532562595Subproblem 2
x + -13 = -11.532562595 Simplifying x + -13 = -11.532562595 Reorder the terms: -13 + x = -11.532562595 Solving -13 + x = -11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -11.532562595 + 13 Combine like terms: -13 + 13 = 0 0 + x = -11.532562595 + 13 x = -11.532562595 + 13 Combine like terms: -11.532562595 + 13 = 1.467437405 x = 1.467437405 Simplifying x = 1.467437405Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.532562595, 1.467437405}
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