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Simplifying x2 + -14x = -29 Reorder the terms: -14x + x2 = -29 Solving -14x + x2 = -29 Solving for variable 'x'. Reorder the terms: 29 + -14x + x2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -14x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + -14x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -14x + x2 = 0 + -29 -14x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 -14x + x2 = -29 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 = -29 + 49 Reorder the terms: 49 + -14x + x2 = -29 + 49 Combine like terms: -29 + 49 = 20 49 + -14x + x2 = 20 Factor a perfect square on the left side: (x + -7)(x + -7) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -7) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -7 = 4.472135955 Simplifying x + -7 = 4.472135955 Reorder the terms: -7 + x = 4.472135955 Solving -7 + x = 4.472135955 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 = 4.472135955 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.472135955 + 7 x = 4.472135955 + 7 Combine like terms: 4.472135955 + 7 = 11.472135955 x = 11.472135955 Simplifying x = 11.472135955Subproblem 2
x + -7 = -4.472135955 Simplifying x + -7 = -4.472135955 Reorder the terms: -7 + x = -4.472135955 Solving -7 + x = -4.472135955 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 = -4.472135955 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.472135955 + 7 x = -4.472135955 + 7 Combine like terms: -4.472135955 + 7 = 2.527864045 x = 2.527864045 Simplifying x = 2.527864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.472135955, 2.527864045}
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