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Simplifying x2 + 26x + -264 = 0 Reorder the terms: -264 + 26x + x2 = 0 Solving -264 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '264' to each side of the equation. -264 + 26x + 264 + x2 = 0 + 264 Reorder the terms: -264 + 264 + 26x + x2 = 0 + 264 Combine like terms: -264 + 264 = 0 0 + 26x + x2 = 0 + 264 26x + x2 = 0 + 264 Combine like terms: 0 + 264 = 264 26x + x2 = 264 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 = 264 + 169 Reorder the terms: 169 + 26x + x2 = 264 + 169 Combine like terms: 264 + 169 = 433 169 + 26x + x2 = 433 Factor a perfect square on the left side: (x + 13)(x + 13) = 433 Calculate the square root of the right side: 20.808652047 Break this problem into two subproblems by setting (x + 13) equal to 20.808652047 and -20.808652047.Subproblem 1
x + 13 = 20.808652047 Simplifying x + 13 = 20.808652047 Reorder the terms: 13 + x = 20.808652047 Solving 13 + x = 20.808652047 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 = 20.808652047 + -13 Combine like terms: 13 + -13 = 0 0 + x = 20.808652047 + -13 x = 20.808652047 + -13 Combine like terms: 20.808652047 + -13 = 7.808652047 x = 7.808652047 Simplifying x = 7.808652047Subproblem 2
x + 13 = -20.808652047 Simplifying x + 13 = -20.808652047 Reorder the terms: 13 + x = -20.808652047 Solving 13 + x = -20.808652047 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 = -20.808652047 + -13 Combine like terms: 13 + -13 = 0 0 + x = -20.808652047 + -13 x = -20.808652047 + -13 Combine like terms: -20.808652047 + -13 = -33.808652047 x = -33.808652047 Simplifying x = -33.808652047Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.808652047, -33.808652047}
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