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Simplifying 7 = -1x2 + 6x + 1 Reorder the terms: 7 = 1 + 6x + -1x2 Solving 7 = 1 + 6x + -1x2 Solving for variable 'x'. Combine like terms: 7 + -1 = 6 6 + -6x + x2 = 1 + 6x + -1x2 + -1 + -6x + x2 Reorder the terms: 6 + -6x + x2 = 1 + -1 + 6x + -6x + -1x2 + x2 Combine like terms: 1 + -1 = 0 6 + -6x + x2 = 0 + 6x + -6x + -1x2 + x2 6 + -6x + x2 = 6x + -6x + -1x2 + x2 Combine like terms: 6x + -6x = 0 6 + -6x + x2 = 0 + -1x2 + x2 6 + -6x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 6 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -6x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6x + x2 = 0 + -6 -6x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6x + x2 = -6 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 = -6 + 9 Reorder the terms: 9 + -6x + x2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + -6x + x2 = 3 Factor a perfect square on the left side: (x + -3)(x + -3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -3) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -3 = 1.732050808 Simplifying x + -3 = 1.732050808 Reorder the terms: -3 + x = 1.732050808 Solving -3 + x = 1.732050808 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 = 1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.732050808 + 3 x = 1.732050808 + 3 Combine like terms: 1.732050808 + 3 = 4.732050808 x = 4.732050808 Simplifying x = 4.732050808Subproblem 2
x + -3 = -1.732050808 Simplifying x + -3 = -1.732050808 Reorder the terms: -3 + x = -1.732050808 Solving -3 + x = -1.732050808 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 = -1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.732050808 + 3 x = -1.732050808 + 3 Combine like terms: -1.732050808 + 3 = 1.267949192 x = 1.267949192 Simplifying x = 1.267949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.732050808, 1.267949192}
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