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Simplifying x2 + x2 + 4x + -109 = 0 Reorder the terms: -109 + 4x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 -109 + 4x + 2x2 = 0 Solving -109 + 4x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -54.5 + 2x + x2 = 0 Move the constant term to the right: Add '54.5' to each side of the equation. -54.5 + 2x + 54.5 + x2 = 0 + 54.5 Reorder the terms: -54.5 + 54.5 + 2x + x2 = 0 + 54.5 Combine like terms: -54.5 + 54.5 = 0.0 0.0 + 2x + x2 = 0 + 54.5 2x + x2 = 0 + 54.5 Combine like terms: 0 + 54.5 = 54.5 2x + x2 = 54.5 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 = 54.5 + 1 Reorder the terms: 1 + 2x + x2 = 54.5 + 1 Combine like terms: 54.5 + 1 = 55.5 1 + 2x + x2 = 55.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 55.5 Calculate the square root of the right side: 7.449832213 Break this problem into two subproblems by setting (x + 1) equal to 7.449832213 and -7.449832213.Subproblem 1
x + 1 = 7.449832213 Simplifying x + 1 = 7.449832213 Reorder the terms: 1 + x = 7.449832213 Solving 1 + x = 7.449832213 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 = 7.449832213 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.449832213 + -1 x = 7.449832213 + -1 Combine like terms: 7.449832213 + -1 = 6.449832213 x = 6.449832213 Simplifying x = 6.449832213Subproblem 2
x + 1 = -7.449832213 Simplifying x + 1 = -7.449832213 Reorder the terms: 1 + x = -7.449832213 Solving 1 + x = -7.449832213 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 = -7.449832213 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.449832213 + -1 x = -7.449832213 + -1 Combine like terms: -7.449832213 + -1 = -8.449832213 x = -8.449832213 Simplifying x = -8.449832213Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.449832213, -8.449832213}
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