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Simplifying x2 + 26x + -0.36 = 0 Reorder the terms: -0.36 + 26x + x2 = 0 Solving -0.36 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + 26x + 0.36 + x2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + 26x + x2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + 26x + x2 = 0 + 0.36 26x + x2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 26x + x2 = 0.36 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 = 0.36 + 169 Reorder the terms: 169 + 26x + x2 = 0.36 + 169 Combine like terms: 0.36 + 169 = 169.36 169 + 26x + x2 = 169.36 Factor a perfect square on the left side: (x + 13)(x + 13) = 169.36 Calculate the square root of the right side: 13.013838788 Break this problem into two subproblems by setting (x + 13) equal to 13.013838788 and -13.013838788.Subproblem 1
x + 13 = 13.013838788 Simplifying x + 13 = 13.013838788 Reorder the terms: 13 + x = 13.013838788 Solving 13 + x = 13.013838788 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 = 13.013838788 + -13 Combine like terms: 13 + -13 = 0 0 + x = 13.013838788 + -13 x = 13.013838788 + -13 Combine like terms: 13.013838788 + -13 = 0.013838788 x = 0.013838788 Simplifying x = 0.013838788Subproblem 2
x + 13 = -13.013838788 Simplifying x + 13 = -13.013838788 Reorder the terms: 13 + x = -13.013838788 Solving 13 + x = -13.013838788 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 = -13.013838788 + -13 Combine like terms: 13 + -13 = 0 0 + x = -13.013838788 + -13 x = -13.013838788 + -13 Combine like terms: -13.013838788 + -13 = -26.013838788 x = -26.013838788 Simplifying x = -26.013838788Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.013838788, -26.013838788}
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