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Simplifying 6x + -8 + x2 = 90 Reorder the terms: -8 + 6x + x2 = 90 Solving -8 + 6x + x2 = 90 Solving for variable 'x'. Reorder the terms: -8 + -90 + 6x + x2 = 90 + -90 Combine like terms: -8 + -90 = -98 -98 + 6x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -98 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + 6x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + 6x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 6x + x2 = 0 + 98 6x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 6x + x2 = 98 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 = 98 + 9 Reorder the terms: 9 + 6x + x2 = 98 + 9 Combine like terms: 98 + 9 = 107 9 + 6x + x2 = 107 Factor a perfect square on the left side: (x + 3)(x + 3) = 107 Calculate the square root of the right side: 10.344080433 Break this problem into two subproblems by setting (x + 3) equal to 10.344080433 and -10.344080433.Subproblem 1
x + 3 = 10.344080433 Simplifying x + 3 = 10.344080433 Reorder the terms: 3 + x = 10.344080433 Solving 3 + x = 10.344080433 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 = 10.344080433 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.344080433 + -3 x = 10.344080433 + -3 Combine like terms: 10.344080433 + -3 = 7.344080433 x = 7.344080433 Simplifying x = 7.344080433Subproblem 2
x + 3 = -10.344080433 Simplifying x + 3 = -10.344080433 Reorder the terms: 3 + x = -10.344080433 Solving 3 + x = -10.344080433 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 = -10.344080433 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.344080433 + -3 x = -10.344080433 + -3 Combine like terms: -10.344080433 + -3 = -13.344080433 x = -13.344080433 Simplifying x = -13.344080433Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.344080433, -13.344080433}
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