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Simplifying x2 + -6x = 51 Reorder the terms: -6x + x2 = 51 Solving -6x + x2 = 51 Solving for variable 'x'. Reorder the terms: -51 + -6x + x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -6x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + -6x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -6x + x2 = 0 + 51 -6x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 -6x + x2 = 51 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 = 51 + 9 Reorder the terms: 9 + -6x + x2 = 51 + 9 Combine like terms: 51 + 9 = 60 9 + -6x + x2 = 60 Factor a perfect square on the left side: (x + -3)(x + -3) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -3) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -3 = 7.745966692 Simplifying x + -3 = 7.745966692 Reorder the terms: -3 + x = 7.745966692 Solving -3 + x = 7.745966692 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 = 7.745966692 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.745966692 + 3 x = 7.745966692 + 3 Combine like terms: 7.745966692 + 3 = 10.745966692 x = 10.745966692 Simplifying x = 10.745966692Subproblem 2
x + -3 = -7.745966692 Simplifying x + -3 = -7.745966692 Reorder the terms: -3 + x = -7.745966692 Solving -3 + x = -7.745966692 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 = -7.745966692 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.745966692 + 3 x = -7.745966692 + 3 Combine like terms: -7.745966692 + 3 = -4.745966692 x = -4.745966692 Simplifying x = -4.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.745966692, -4.745966692}
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