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Simplifying x2 + -6x + -37 = 6 Reorder the terms: -37 + -6x + x2 = 6 Solving -37 + -6x + x2 = 6 Solving for variable 'x'. Reorder the terms: -37 + -6 + -6x + x2 = 6 + -6 Combine like terms: -37 + -6 = -43 -43 + -6x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -43 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -6x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + -6x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -6x + x2 = 0 + 43 -6x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 -6x + x2 = 43 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 = 43 + 9 Reorder the terms: 9 + -6x + x2 = 43 + 9 Combine like terms: 43 + 9 = 52 9 + -6x + x2 = 52 Factor a perfect square on the left side: (x + -3)(x + -3) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + -3) equal to 7.211102551 and -7.211102551.Subproblem 1
x + -3 = 7.211102551 Simplifying x + -3 = 7.211102551 Reorder the terms: -3 + x = 7.211102551 Solving -3 + x = 7.211102551 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 = 7.211102551 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.211102551 + 3 x = 7.211102551 + 3 Combine like terms: 7.211102551 + 3 = 10.211102551 x = 10.211102551 Simplifying x = 10.211102551Subproblem 2
x + -3 = -7.211102551 Simplifying x + -3 = -7.211102551 Reorder the terms: -3 + x = -7.211102551 Solving -3 + x = -7.211102551 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 = -7.211102551 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.211102551 + 3 x = -7.211102551 + 3 Combine like terms: -7.211102551 + 3 = -4.211102551 x = -4.211102551 Simplifying x = -4.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.211102551, -4.211102551}
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