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Simplifying x2 + -6x + -97 = -2 Reorder the terms: -97 + -6x + x2 = -2 Solving -97 + -6x + x2 = -2 Solving for variable 'x'. Reorder the terms: -97 + 2 + -6x + x2 = -2 + 2 Combine like terms: -97 + 2 = -95 -95 + -6x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 -95 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + -6x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + -6x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + -6x + x2 = 0 + 95 -6x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 -6x + x2 = 95 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 = 95 + 9 Reorder the terms: 9 + -6x + x2 = 95 + 9 Combine like terms: 95 + 9 = 104 9 + -6x + x2 = 104 Factor a perfect square on the left side: (x + -3)(x + -3) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (x + -3) equal to 10.198039027 and -10.198039027.Subproblem 1
x + -3 = 10.198039027 Simplifying x + -3 = 10.198039027 Reorder the terms: -3 + x = 10.198039027 Solving -3 + x = 10.198039027 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 = 10.198039027 + 3 Combine like terms: -3 + 3 = 0 0 + x = 10.198039027 + 3 x = 10.198039027 + 3 Combine like terms: 10.198039027 + 3 = 13.198039027 x = 13.198039027 Simplifying x = 13.198039027Subproblem 2
x + -3 = -10.198039027 Simplifying x + -3 = -10.198039027 Reorder the terms: -3 + x = -10.198039027 Solving -3 + x = -10.198039027 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 = -10.198039027 + 3 Combine like terms: -3 + 3 = 0 0 + x = -10.198039027 + 3 x = -10.198039027 + 3 Combine like terms: -10.198039027 + 3 = -7.198039027 x = -7.198039027 Simplifying x = -7.198039027Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.198039027, -7.198039027}
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