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Simplifying x2 + -14x + -60 = 0 Reorder the terms: -60 + -14x + x2 = 0 Solving -60 + -14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -14x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -14x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -14x + x2 = 0 + 60 -14x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -14x + x2 = 60 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 60 + 49 Reorder the terms: 49 + -14x + x2 = 60 + 49 Combine like terms: 60 + 49 = 109 49 + -14x + x2 = 109 Factor a perfect square on the left side: (x + -7)(x + -7) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + -7) equal to 10.440306509 and -10.440306509.Subproblem 1
x + -7 = 10.440306509 Simplifying x + -7 = 10.440306509 Reorder the terms: -7 + x = 10.440306509 Solving -7 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 10.440306509 + 7 Combine like terms: -7 + 7 = 0 0 + x = 10.440306509 + 7 x = 10.440306509 + 7 Combine like terms: 10.440306509 + 7 = 17.440306509 x = 17.440306509 Simplifying x = 17.440306509Subproblem 2
x + -7 = -10.440306509 Simplifying x + -7 = -10.440306509 Reorder the terms: -7 + x = -10.440306509 Solving -7 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -10.440306509 + 7 Combine like terms: -7 + 7 = 0 0 + x = -10.440306509 + 7 x = -10.440306509 + 7 Combine like terms: -10.440306509 + 7 = -3.440306509 x = -3.440306509 Simplifying x = -3.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.440306509, -3.440306509}
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