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Simplifying x2 + -14x = 241 Reorder the terms: -14x + x2 = 241 Solving -14x + x2 = 241 Solving for variable 'x'. Reorder the terms: -241 + -14x + x2 = 241 + -241 Combine like terms: 241 + -241 = 0 -241 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '241' to each side of the equation. -241 + -14x + 241 + x2 = 0 + 241 Reorder the terms: -241 + 241 + -14x + x2 = 0 + 241 Combine like terms: -241 + 241 = 0 0 + -14x + x2 = 0 + 241 -14x + x2 = 0 + 241 Combine like terms: 0 + 241 = 241 -14x + x2 = 241 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 = 241 + 49 Reorder the terms: 49 + -14x + x2 = 241 + 49 Combine like terms: 241 + 49 = 290 49 + -14x + x2 = 290 Factor a perfect square on the left side: (x + -7)(x + -7) = 290 Calculate the square root of the right side: 17.029386366 Break this problem into two subproblems by setting (x + -7) equal to 17.029386366 and -17.029386366.Subproblem 1
x + -7 = 17.029386366 Simplifying x + -7 = 17.029386366 Reorder the terms: -7 + x = 17.029386366 Solving -7 + x = 17.029386366 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 = 17.029386366 + 7 Combine like terms: -7 + 7 = 0 0 + x = 17.029386366 + 7 x = 17.029386366 + 7 Combine like terms: 17.029386366 + 7 = 24.029386366 x = 24.029386366 Simplifying x = 24.029386366Subproblem 2
x + -7 = -17.029386366 Simplifying x + -7 = -17.029386366 Reorder the terms: -7 + x = -17.029386366 Solving -7 + x = -17.029386366 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 = -17.029386366 + 7 Combine like terms: -7 + 7 = 0 0 + x = -17.029386366 + 7 x = -17.029386366 + 7 Combine like terms: -17.029386366 + 7 = -10.029386366 x = -10.029386366 Simplifying x = -10.029386366Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.029386366, -10.029386366}
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