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Simplifying x2 + -14x = 226 Reorder the terms: -14x + x2 = 226 Solving -14x + x2 = 226 Solving for variable 'x'. Reorder the terms: -226 + -14x + x2 = 226 + -226 Combine like terms: 226 + -226 = 0 -226 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '226' to each side of the equation. -226 + -14x + 226 + x2 = 0 + 226 Reorder the terms: -226 + 226 + -14x + x2 = 0 + 226 Combine like terms: -226 + 226 = 0 0 + -14x + x2 = 0 + 226 -14x + x2 = 0 + 226 Combine like terms: 0 + 226 = 226 -14x + x2 = 226 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 = 226 + 49 Reorder the terms: 49 + -14x + x2 = 226 + 49 Combine like terms: 226 + 49 = 275 49 + -14x + x2 = 275 Factor a perfect square on the left side: (x + -7)(x + -7) = 275 Calculate the square root of the right side: 16.583123952 Break this problem into two subproblems by setting (x + -7) equal to 16.583123952 and -16.583123952.Subproblem 1
x + -7 = 16.583123952 Simplifying x + -7 = 16.583123952 Reorder the terms: -7 + x = 16.583123952 Solving -7 + x = 16.583123952 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 = 16.583123952 + 7 Combine like terms: -7 + 7 = 0 0 + x = 16.583123952 + 7 x = 16.583123952 + 7 Combine like terms: 16.583123952 + 7 = 23.583123952 x = 23.583123952 Simplifying x = 23.583123952Subproblem 2
x + -7 = -16.583123952 Simplifying x + -7 = -16.583123952 Reorder the terms: -7 + x = -16.583123952 Solving -7 + x = -16.583123952 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 = -16.583123952 + 7 Combine like terms: -7 + 7 = 0 0 + x = -16.583123952 + 7 x = -16.583123952 + 7 Combine like terms: -16.583123952 + 7 = -9.583123952 x = -9.583123952 Simplifying x = -9.583123952Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.583123952, -9.583123952}
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