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Simplifying x2 + 25x + 6 + 6x + 30 + -3 = 0 Reorder the terms: 6 + 30 + -3 + 25x + 6x + x2 = 0 Combine like terms: 6 + 30 = 36 36 + -3 + 25x + 6x + x2 = 0 Combine like terms: 36 + -3 = 33 33 + 25x + 6x + x2 = 0 Combine like terms: 25x + 6x = 31x 33 + 31x + x2 = 0 Solving 33 + 31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + 31x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + 31x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 31x + x2 = 0 + -33 31x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 31x + x2 = -33 The x term is 31x. Take half its coefficient (15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. 31x + 240.25 + x2 = -33 + 240.25 Reorder the terms: 240.25 + 31x + x2 = -33 + 240.25 Combine like terms: -33 + 240.25 = 207.25 240.25 + 31x + x2 = 207.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 207.25 Calculate the square root of the right side: 14.396180049 Break this problem into two subproblems by setting (x + 15.5) equal to 14.396180049 and -14.396180049.Subproblem 1
x + 15.5 = 14.396180049 Simplifying x + 15.5 = 14.396180049 Reorder the terms: 15.5 + x = 14.396180049 Solving 15.5 + x = 14.396180049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 14.396180049 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 14.396180049 + -15.5 x = 14.396180049 + -15.5 Combine like terms: 14.396180049 + -15.5 = -1.103819951 x = -1.103819951 Simplifying x = -1.103819951Subproblem 2
x + 15.5 = -14.396180049 Simplifying x + 15.5 = -14.396180049 Reorder the terms: 15.5 + x = -14.396180049 Solving 15.5 + x = -14.396180049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -14.396180049 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -14.396180049 + -15.5 x = -14.396180049 + -15.5 Combine like terms: -14.396180049 + -15.5 = -29.896180049 x = -29.896180049 Simplifying x = -29.896180049Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.103819951, -29.896180049}
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