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Simplifying x2 + 45x + 2 = 3x + 6 Reorder the terms: 2 + 45x + x2 = 3x + 6 Reorder the terms: 2 + 45x + x2 = 6 + 3x Solving 2 + 45x + x2 = 6 + 3x Solving for variable 'x'. Reorder the terms: 2 + -6 + 45x + -3x + x2 = 6 + 3x + -6 + -3x Combine like terms: 2 + -6 = -4 -4 + 45x + -3x + x2 = 6 + 3x + -6 + -3x Combine like terms: 45x + -3x = 42x -4 + 42x + x2 = 6 + 3x + -6 + -3x Reorder the terms: -4 + 42x + x2 = 6 + -6 + 3x + -3x Combine like terms: 6 + -6 = 0 -4 + 42x + x2 = 0 + 3x + -3x -4 + 42x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -4 + 42x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 42x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 42x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 42x + x2 = 0 + 4 42x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 42x + x2 = 4 The x term is 42x. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42x + 441 + x2 = 4 + 441 Reorder the terms: 441 + 42x + x2 = 4 + 441 Combine like terms: 4 + 441 = 445 441 + 42x + x2 = 445 Factor a perfect square on the left side: (x + 21)(x + 21) = 445 Calculate the square root of the right side: 21.09502311 Break this problem into two subproblems by setting (x + 21) equal to 21.09502311 and -21.09502311.Subproblem 1
x + 21 = 21.09502311 Simplifying x + 21 = 21.09502311 Reorder the terms: 21 + x = 21.09502311 Solving 21 + x = 21.09502311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 21.09502311 + -21 Combine like terms: 21 + -21 = 0 0 + x = 21.09502311 + -21 x = 21.09502311 + -21 Combine like terms: 21.09502311 + -21 = 0.09502311 x = 0.09502311 Simplifying x = 0.09502311Subproblem 2
x + 21 = -21.09502311 Simplifying x + 21 = -21.09502311 Reorder the terms: 21 + x = -21.09502311 Solving 21 + x = -21.09502311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = -21.09502311 + -21 Combine like terms: 21 + -21 = 0 0 + x = -21.09502311 + -21 x = -21.09502311 + -21 Combine like terms: -21.09502311 + -21 = -42.09502311 x = -42.09502311 Simplifying x = -42.09502311Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.09502311, -42.09502311}
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