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Simplifying x2 + -6x + -91 = 10 Reorder the terms: -91 + -6x + x2 = 10 Solving -91 + -6x + x2 = 10 Solving for variable 'x'. Reorder the terms: -91 + -10 + -6x + x2 = 10 + -10 Combine like terms: -91 + -10 = -101 -101 + -6x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -101 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '101' to each side of the equation. -101 + -6x + 101 + x2 = 0 + 101 Reorder the terms: -101 + 101 + -6x + x2 = 0 + 101 Combine like terms: -101 + 101 = 0 0 + -6x + x2 = 0 + 101 -6x + x2 = 0 + 101 Combine like terms: 0 + 101 = 101 -6x + x2 = 101 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 = 101 + 9 Reorder the terms: 9 + -6x + x2 = 101 + 9 Combine like terms: 101 + 9 = 110 9 + -6x + x2 = 110 Factor a perfect square on the left side: (x + -3)(x + -3) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x + -3) equal to 10.488088482 and -10.488088482.Subproblem 1
x + -3 = 10.488088482 Simplifying x + -3 = 10.488088482 Reorder the terms: -3 + x = 10.488088482 Solving -3 + x = 10.488088482 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 = 10.488088482 + 3 Combine like terms: -3 + 3 = 0 0 + x = 10.488088482 + 3 x = 10.488088482 + 3 Combine like terms: 10.488088482 + 3 = 13.488088482 x = 13.488088482 Simplifying x = 13.488088482Subproblem 2
x + -3 = -10.488088482 Simplifying x + -3 = -10.488088482 Reorder the terms: -3 + x = -10.488088482 Solving -3 + x = -10.488088482 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 = -10.488088482 + 3 Combine like terms: -3 + 3 = 0 0 + x = -10.488088482 + 3 x = -10.488088482 + 3 Combine like terms: -10.488088482 + 3 = -7.488088482 x = -7.488088482 Simplifying x = -7.488088482Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.488088482, -7.488088482}
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