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Simplifying x2 + -6x + -7 = 398 Reorder the terms: -7 + -6x + x2 = 398 Solving -7 + -6x + x2 = 398 Solving for variable 'x'. Reorder the terms: -7 + -398 + -6x + x2 = 398 + -398 Combine like terms: -7 + -398 = -405 -405 + -6x + x2 = 398 + -398 Combine like terms: 398 + -398 = 0 -405 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '405' to each side of the equation. -405 + -6x + 405 + x2 = 0 + 405 Reorder the terms: -405 + 405 + -6x + x2 = 0 + 405 Combine like terms: -405 + 405 = 0 0 + -6x + x2 = 0 + 405 -6x + x2 = 0 + 405 Combine like terms: 0 + 405 = 405 -6x + x2 = 405 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 = 405 + 9 Reorder the terms: 9 + -6x + x2 = 405 + 9 Combine like terms: 405 + 9 = 414 9 + -6x + x2 = 414 Factor a perfect square on the left side: (x + -3)(x + -3) = 414 Calculate the square root of the right side: 20.346989949 Break this problem into two subproblems by setting (x + -3) equal to 20.346989949 and -20.346989949.Subproblem 1
x + -3 = 20.346989949 Simplifying x + -3 = 20.346989949 Reorder the terms: -3 + x = 20.346989949 Solving -3 + x = 20.346989949 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 = 20.346989949 + 3 Combine like terms: -3 + 3 = 0 0 + x = 20.346989949 + 3 x = 20.346989949 + 3 Combine like terms: 20.346989949 + 3 = 23.346989949 x = 23.346989949 Simplifying x = 23.346989949Subproblem 2
x + -3 = -20.346989949 Simplifying x + -3 = -20.346989949 Reorder the terms: -3 + x = -20.346989949 Solving -3 + x = -20.346989949 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 = -20.346989949 + 3 Combine like terms: -3 + 3 = 0 0 + x = -20.346989949 + 3 x = -20.346989949 + 3 Combine like terms: -20.346989949 + 3 = -17.346989949 x = -17.346989949 Simplifying x = -17.346989949Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.346989949, -17.346989949}
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