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Simplifying x2 + 12x = 136 Reorder the terms: 12x + x2 = 136 Solving 12x + x2 = 136 Solving for variable 'x'. Reorder the terms: -136 + 12x + x2 = 136 + -136 Combine like terms: 136 + -136 = 0 -136 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + 12x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + 12x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + 12x + x2 = 0 + 136 12x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 12x + x2 = 136 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 = 136 + 36 Reorder the terms: 36 + 12x + x2 = 136 + 36 Combine like terms: 136 + 36 = 172 36 + 12x + x2 = 172 Factor a perfect square on the left side: (x + 6)(x + 6) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (x + 6) equal to 13.114877049 and -13.114877049.Subproblem 1
x + 6 = 13.114877049 Simplifying x + 6 = 13.114877049 Reorder the terms: 6 + x = 13.114877049 Solving 6 + x = 13.114877049 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 = 13.114877049 + -6 Combine like terms: 6 + -6 = 0 0 + x = 13.114877049 + -6 x = 13.114877049 + -6 Combine like terms: 13.114877049 + -6 = 7.114877049 x = 7.114877049 Simplifying x = 7.114877049Subproblem 2
x + 6 = -13.114877049 Simplifying x + 6 = -13.114877049 Reorder the terms: 6 + x = -13.114877049 Solving 6 + x = -13.114877049 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 = -13.114877049 + -6 Combine like terms: 6 + -6 = 0 0 + x = -13.114877049 + -6 x = -13.114877049 + -6 Combine like terms: -13.114877049 + -6 = -19.114877049 x = -19.114877049 Simplifying x = -19.114877049Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.114877049, -19.114877049}
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