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Simplifying x2 + -6x = 49 Reorder the terms: -6x + x2 = 49 Solving -6x + x2 = 49 Solving for variable 'x'. Reorder the terms: -49 + -6x + x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -6x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -6x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -6x + x2 = 0 + 49 -6x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -6x + x2 = 49 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 = 49 + 9 Reorder the terms: 9 + -6x + x2 = 49 + 9 Combine like terms: 49 + 9 = 58 9 + -6x + x2 = 58 Factor a perfect square on the left side: (x + -3)(x + -3) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + -3) equal to 7.615773106 and -7.615773106.Subproblem 1
x + -3 = 7.615773106 Simplifying x + -3 = 7.615773106 Reorder the terms: -3 + x = 7.615773106 Solving -3 + x = 7.615773106 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 = 7.615773106 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.615773106 + 3 x = 7.615773106 + 3 Combine like terms: 7.615773106 + 3 = 10.615773106 x = 10.615773106 Simplifying x = 10.615773106Subproblem 2
x + -3 = -7.615773106 Simplifying x + -3 = -7.615773106 Reorder the terms: -3 + x = -7.615773106 Solving -3 + x = -7.615773106 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 = -7.615773106 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.615773106 + 3 x = -7.615773106 + 3 Combine like terms: -7.615773106 + 3 = -4.615773106 x = -4.615773106 Simplifying x = -4.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.615773106, -4.615773106}
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