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Simplifying x2 + 14x = 321 Reorder the terms: 14x + x2 = 321 Solving 14x + x2 = 321 Solving for variable 'x'. Reorder the terms: -321 + 14x + x2 = 321 + -321 Combine like terms: 321 + -321 = 0 -321 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '321' to each side of the equation. -321 + 14x + 321 + x2 = 0 + 321 Reorder the terms: -321 + 321 + 14x + x2 = 0 + 321 Combine like terms: -321 + 321 = 0 0 + 14x + x2 = 0 + 321 14x + x2 = 0 + 321 Combine like terms: 0 + 321 = 321 14x + x2 = 321 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 = 321 + 49 Reorder the terms: 49 + 14x + x2 = 321 + 49 Combine like terms: 321 + 49 = 370 49 + 14x + x2 = 370 Factor a perfect square on the left side: (x + 7)(x + 7) = 370 Calculate the square root of the right side: 19.235384062 Break this problem into two subproblems by setting (x + 7) equal to 19.235384062 and -19.235384062.Subproblem 1
x + 7 = 19.235384062 Simplifying x + 7 = 19.235384062 Reorder the terms: 7 + x = 19.235384062 Solving 7 + x = 19.235384062 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 = 19.235384062 + -7 Combine like terms: 7 + -7 = 0 0 + x = 19.235384062 + -7 x = 19.235384062 + -7 Combine like terms: 19.235384062 + -7 = 12.235384062 x = 12.235384062 Simplifying x = 12.235384062Subproblem 2
x + 7 = -19.235384062 Simplifying x + 7 = -19.235384062 Reorder the terms: 7 + x = -19.235384062 Solving 7 + x = -19.235384062 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 = -19.235384062 + -7 Combine like terms: 7 + -7 = 0 0 + x = -19.235384062 + -7 x = -19.235384062 + -7 Combine like terms: -19.235384062 + -7 = -26.235384062 x = -26.235384062 Simplifying x = -26.235384062Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.235384062, -26.235384062}
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