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Simplifying x2 + 2x + -65 = 4 Reorder the terms: -65 + 2x + x2 = 4 Solving -65 + 2x + x2 = 4 Solving for variable 'x'. Reorder the terms: -65 + -4 + 2x + x2 = 4 + -4 Combine like terms: -65 + -4 = -69 -69 + 2x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -69 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + 2x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + 2x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + 2x + x2 = 0 + 69 2x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 2x + x2 = 69 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 69 + 1 Reorder the terms: 1 + 2x + x2 = 69 + 1 Combine like terms: 69 + 1 = 70 1 + 2x + x2 = 70 Factor a perfect square on the left side: (x + 1)(x + 1) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + 1) equal to 8.366600265 and -8.366600265.Subproblem 1
x + 1 = 8.366600265 Simplifying x + 1 = 8.366600265 Reorder the terms: 1 + x = 8.366600265 Solving 1 + x = 8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 8.366600265 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.366600265 + -1 x = 8.366600265 + -1 Combine like terms: 8.366600265 + -1 = 7.366600265 x = 7.366600265 Simplifying x = 7.366600265Subproblem 2
x + 1 = -8.366600265 Simplifying x + 1 = -8.366600265 Reorder the terms: 1 + x = -8.366600265 Solving 1 + x = -8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -8.366600265 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.366600265 + -1 x = -8.366600265 + -1 Combine like terms: -8.366600265 + -1 = -9.366600265 x = -9.366600265 Simplifying x = -9.366600265Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.366600265, -9.366600265}
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