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Simplifying x2 + -14x = -5 Reorder the terms: -14x + x2 = -5 Solving -14x + x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + -14x + x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -14x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -14x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -14x + x2 = 0 + -5 -14x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -14x + x2 = -5 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 = -5 + 49 Reorder the terms: 49 + -14x + x2 = -5 + 49 Combine like terms: -5 + 49 = 44 49 + -14x + x2 = 44 Factor a perfect square on the left side: (x + -7)(x + -7) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + -7) equal to 6.633249581 and -6.633249581.Subproblem 1
x + -7 = 6.633249581 Simplifying x + -7 = 6.633249581 Reorder the terms: -7 + x = 6.633249581 Solving -7 + x = 6.633249581 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 = 6.633249581 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.633249581 + 7 x = 6.633249581 + 7 Combine like terms: 6.633249581 + 7 = 13.633249581 x = 13.633249581 Simplifying x = 13.633249581Subproblem 2
x + -7 = -6.633249581 Simplifying x + -7 = -6.633249581 Reorder the terms: -7 + x = -6.633249581 Solving -7 + x = -6.633249581 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 = -6.633249581 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.633249581 + 7 x = -6.633249581 + 7 Combine like terms: -6.633249581 + 7 = 0.366750419 x = 0.366750419 Simplifying x = 0.366750419Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.633249581, 0.366750419}
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