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Simplifying x2 + -14x = -11 Reorder the terms: -14x + x2 = -11 Solving -14x + x2 = -11 Solving for variable 'x'. Reorder the terms: 11 + -14x + x2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -14x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -14x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -14x + x2 = 0 + -11 -14x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -14x + x2 = -11 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 = -11 + 49 Reorder the terms: 49 + -14x + x2 = -11 + 49 Combine like terms: -11 + 49 = 38 49 + -14x + x2 = 38 Factor a perfect square on the left side: (x + -7)(x + -7) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + -7) equal to 6.164414003 and -6.164414003.Subproblem 1
x + -7 = 6.164414003 Simplifying x + -7 = 6.164414003 Reorder the terms: -7 + x = 6.164414003 Solving -7 + x = 6.164414003 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 = 6.164414003 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.164414003 + 7 x = 6.164414003 + 7 Combine like terms: 6.164414003 + 7 = 13.164414003 x = 13.164414003 Simplifying x = 13.164414003Subproblem 2
x + -7 = -6.164414003 Simplifying x + -7 = -6.164414003 Reorder the terms: -7 + x = -6.164414003 Solving -7 + x = -6.164414003 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 = -6.164414003 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.164414003 + 7 x = -6.164414003 + 7 Combine like terms: -6.164414003 + 7 = 0.835585997 x = 0.835585997 Simplifying x = 0.835585997Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.164414003, 0.835585997}
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