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Simplifying x2 + -9 = 6x + -5 Reorder the terms: -9 + x2 = 6x + -5 Reorder the terms: -9 + x2 = -5 + 6x Solving -9 + x2 = -5 + 6x Solving for variable 'x'. Reorder the terms: -9 + 5 + -6x + x2 = -5 + 6x + 5 + -6x Combine like terms: -9 + 5 = -4 -4 + -6x + x2 = -5 + 6x + 5 + -6x Reorder the terms: -4 + -6x + x2 = -5 + 5 + 6x + -6x Combine like terms: -5 + 5 = 0 -4 + -6x + x2 = 0 + 6x + -6x -4 + -6x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -4 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -6x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -6x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6x + x2 = 0 + 4 -6x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6x + x2 = 4 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 = 4 + 9 Reorder the terms: 9 + -6x + x2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + -6x + x2 = 13 Factor a perfect square on the left side: (x + -3)(x + -3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -3) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -3 = 3.605551275 Simplifying x + -3 = 3.605551275 Reorder the terms: -3 + x = 3.605551275 Solving -3 + x = 3.605551275 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 = 3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.605551275 + 3 x = 3.605551275 + 3 Combine like terms: 3.605551275 + 3 = 6.605551275 x = 6.605551275 Simplifying x = 6.605551275Subproblem 2
x + -3 = -3.605551275 Simplifying x + -3 = -3.605551275 Reorder the terms: -3 + x = -3.605551275 Solving -3 + x = -3.605551275 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 = -3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.605551275 + 3 x = -3.605551275 + 3 Combine like terms: -3.605551275 + 3 = -0.605551275 x = -0.605551275 Simplifying x = -0.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.605551275, -0.605551275}
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