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Simplifying x2 + 4x + -765 = 0 Reorder the terms: -765 + 4x + x2 = 0 Solving -765 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '765' to each side of the equation. -765 + 4x + 765 + x2 = 0 + 765 Reorder the terms: -765 + 765 + 4x + x2 = 0 + 765 Combine like terms: -765 + 765 = 0 0 + 4x + x2 = 0 + 765 4x + x2 = 0 + 765 Combine like terms: 0 + 765 = 765 4x + x2 = 765 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 765 + 4 Reorder the terms: 4 + 4x + x2 = 765 + 4 Combine like terms: 765 + 4 = 769 4 + 4x + x2 = 769 Factor a perfect square on the left side: (x + 2)(x + 2) = 769 Calculate the square root of the right side: 27.730849248 Break this problem into two subproblems by setting (x + 2) equal to 27.730849248 and -27.730849248.Subproblem 1
x + 2 = 27.730849248 Simplifying x + 2 = 27.730849248 Reorder the terms: 2 + x = 27.730849248 Solving 2 + x = 27.730849248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 27.730849248 + -2 Combine like terms: 2 + -2 = 0 0 + x = 27.730849248 + -2 x = 27.730849248 + -2 Combine like terms: 27.730849248 + -2 = 25.730849248 x = 25.730849248 Simplifying x = 25.730849248Subproblem 2
x + 2 = -27.730849248 Simplifying x + 2 = -27.730849248 Reorder the terms: 2 + x = -27.730849248 Solving 2 + x = -27.730849248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -27.730849248 + -2 Combine like terms: 2 + -2 = 0 0 + x = -27.730849248 + -2 x = -27.730849248 + -2 Combine like terms: -27.730849248 + -2 = -29.730849248 x = -29.730849248 Simplifying x = -29.730849248Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.730849248, -29.730849248}
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