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Simplifying x2 + -14x + -91 = 0 Reorder the terms: -91 + -14x + x2 = 0 Solving -91 + -14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + -14x + 91 + x2 = 0 + 91 Reorder the terms: -91 + 91 + -14x + x2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + -14x + x2 = 0 + 91 -14x + x2 = 0 + 91 Combine like terms: 0 + 91 = 91 -14x + x2 = 91 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 = 91 + 49 Reorder the terms: 49 + -14x + x2 = 91 + 49 Combine like terms: 91 + 49 = 140 49 + -14x + x2 = 140 Factor a perfect square on the left side: (x + -7)(x + -7) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (x + -7) equal to 11.832159566 and -11.832159566.Subproblem 1
x + -7 = 11.832159566 Simplifying x + -7 = 11.832159566 Reorder the terms: -7 + x = 11.832159566 Solving -7 + x = 11.832159566 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 = 11.832159566 + 7 Combine like terms: -7 + 7 = 0 0 + x = 11.832159566 + 7 x = 11.832159566 + 7 Combine like terms: 11.832159566 + 7 = 18.832159566 x = 18.832159566 Simplifying x = 18.832159566Subproblem 2
x + -7 = -11.832159566 Simplifying x + -7 = -11.832159566 Reorder the terms: -7 + x = -11.832159566 Solving -7 + x = -11.832159566 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 = -11.832159566 + 7 Combine like terms: -7 + 7 = 0 0 + x = -11.832159566 + 7 x = -11.832159566 + 7 Combine like terms: -11.832159566 + 7 = -4.832159566 x = -4.832159566 Simplifying x = -4.832159566Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.832159566, -4.832159566}
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