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Simplifying x2 + 5x + -1(6 + -1x) = 40 x2 + 5x + (6 * -1 + -1x * -1) = 40 x2 + 5x + (-6 + 1x) = 40 Reorder the terms: -6 + 5x + 1x + x2 = 40 Combine like terms: 5x + 1x = 6x -6 + 6x + x2 = 40 Solving -6 + 6x + x2 = 40 Solving for variable 'x'. Reorder the terms: -6 + -40 + 6x + x2 = 40 + -40 Combine like terms: -6 + -40 = -46 -46 + 6x + x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -46 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 6x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + 6x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 6x + x2 = 0 + 46 6x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 6x + x2 = 46 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 46 + 9 Reorder the terms: 9 + 6x + x2 = 46 + 9 Combine like terms: 46 + 9 = 55 9 + 6x + x2 = 55 Factor a perfect square on the left side: (x + 3)(x + 3) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + 3) equal to 7.416198487 and -7.416198487.Subproblem 1
x + 3 = 7.416198487 Simplifying x + 3 = 7.416198487 Reorder the terms: 3 + x = 7.416198487 Solving 3 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.416198487 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.416198487 + -3 x = 7.416198487 + -3 Combine like terms: 7.416198487 + -3 = 4.416198487 x = 4.416198487 Simplifying x = 4.416198487Subproblem 2
x + 3 = -7.416198487 Simplifying x + 3 = -7.416198487 Reorder the terms: 3 + x = -7.416198487 Solving 3 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.416198487 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.416198487 + -3 x = -7.416198487 + -3 Combine like terms: -7.416198487 + -3 = -10.416198487 x = -10.416198487 Simplifying x = -10.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.416198487, -10.416198487}
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