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Simplifying x2 + -6x + -94 = 0 Reorder the terms: -94 + -6x + x2 = 0 Solving -94 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '94' to each side of the equation. -94 + -6x + 94 + x2 = 0 + 94 Reorder the terms: -94 + 94 + -6x + x2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + -6x + x2 = 0 + 94 -6x + x2 = 0 + 94 Combine like terms: 0 + 94 = 94 -6x + x2 = 94 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 = 94 + 9 Reorder the terms: 9 + -6x + x2 = 94 + 9 Combine like terms: 94 + 9 = 103 9 + -6x + x2 = 103 Factor a perfect square on the left side: (x + -3)(x + -3) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (x + -3) equal to 10.148891565 and -10.148891565.Subproblem 1
x + -3 = 10.148891565 Simplifying x + -3 = 10.148891565 Reorder the terms: -3 + x = 10.148891565 Solving -3 + x = 10.148891565 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 = 10.148891565 + 3 Combine like terms: -3 + 3 = 0 0 + x = 10.148891565 + 3 x = 10.148891565 + 3 Combine like terms: 10.148891565 + 3 = 13.148891565 x = 13.148891565 Simplifying x = 13.148891565Subproblem 2
x + -3 = -10.148891565 Simplifying x + -3 = -10.148891565 Reorder the terms: -3 + x = -10.148891565 Solving -3 + x = -10.148891565 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 = -10.148891565 + 3 Combine like terms: -3 + 3 = 0 0 + x = -10.148891565 + 3 x = -10.148891565 + 3 Combine like terms: -10.148891565 + 3 = -7.148891565 x = -7.148891565 Simplifying x = -7.148891565Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.148891565, -7.148891565}
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