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Simplifying x2 + 529x + -65 = 0 Reorder the terms: -65 + 529x + x2 = 0 Solving -65 + 529x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 529x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + 529x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 529x + x2 = 0 + 65 529x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 529x + x2 = 65 The x term is 529x. Take half its coefficient (264.5). Square it (69960.25) and add it to both sides. Add '69960.25' to each side of the equation. 529x + 69960.25 + x2 = 65 + 69960.25 Reorder the terms: 69960.25 + 529x + x2 = 65 + 69960.25 Combine like terms: 65 + 69960.25 = 70025.25 69960.25 + 529x + x2 = 70025.25 Factor a perfect square on the left side: (x + 264.5)(x + 264.5) = 70025.25 Calculate the square root of the right side: 264.622844819 Break this problem into two subproblems by setting (x + 264.5) equal to 264.622844819 and -264.622844819.Subproblem 1
x + 264.5 = 264.622844819 Simplifying x + 264.5 = 264.622844819 Reorder the terms: 264.5 + x = 264.622844819 Solving 264.5 + x = 264.622844819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-264.5' to each side of the equation. 264.5 + -264.5 + x = 264.622844819 + -264.5 Combine like terms: 264.5 + -264.5 = 0.0 0.0 + x = 264.622844819 + -264.5 x = 264.622844819 + -264.5 Combine like terms: 264.622844819 + -264.5 = 0.122844819 x = 0.122844819 Simplifying x = 0.122844819Subproblem 2
x + 264.5 = -264.622844819 Simplifying x + 264.5 = -264.622844819 Reorder the terms: 264.5 + x = -264.622844819 Solving 264.5 + x = -264.622844819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-264.5' to each side of the equation. 264.5 + -264.5 + x = -264.622844819 + -264.5 Combine like terms: 264.5 + -264.5 = 0.0 0.0 + x = -264.622844819 + -264.5 x = -264.622844819 + -264.5 Combine like terms: -264.622844819 + -264.5 = -529.122844819 x = -529.122844819 Simplifying x = -529.122844819Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.122844819, -529.122844819}
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