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Simplifying x2 + 26x + 53 = 0 Reorder the terms: 53 + 26x + x2 = 0 Solving 53 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 26x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + 26x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 26x + x2 = 0 + -53 26x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 26x + x2 = -53 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 = -53 + 169 Reorder the terms: 169 + 26x + x2 = -53 + 169 Combine like terms: -53 + 169 = 116 169 + 26x + x2 = 116 Factor a perfect square on the left side: (x + 13)(x + 13) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + 13) equal to 10.770329614 and -10.770329614.Subproblem 1
x + 13 = 10.770329614 Simplifying x + 13 = 10.770329614 Reorder the terms: 13 + x = 10.770329614 Solving 13 + x = 10.770329614 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 = 10.770329614 + -13 Combine like terms: 13 + -13 = 0 0 + x = 10.770329614 + -13 x = 10.770329614 + -13 Combine like terms: 10.770329614 + -13 = -2.229670386 x = -2.229670386 Simplifying x = -2.229670386Subproblem 2
x + 13 = -10.770329614 Simplifying x + 13 = -10.770329614 Reorder the terms: 13 + x = -10.770329614 Solving 13 + x = -10.770329614 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 = -10.770329614 + -13 Combine like terms: 13 + -13 = 0 0 + x = -10.770329614 + -13 x = -10.770329614 + -13 Combine like terms: -10.770329614 + -13 = -23.770329614 x = -23.770329614 Simplifying x = -23.770329614Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.229670386, -23.770329614}
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