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Simplifying x2 + -14x + -19 = 1 Reorder the terms: -19 + -14x + x2 = 1 Solving -19 + -14x + x2 = 1 Solving for variable 'x'. Reorder the terms: -19 + -1 + -14x + x2 = 1 + -1 Combine like terms: -19 + -1 = -20 -20 + -14x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -20 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -14x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -14x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -14x + x2 = 0 + 20 -14x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -14x + x2 = 20 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 = 20 + 49 Reorder the terms: 49 + -14x + x2 = 20 + 49 Combine like terms: 20 + 49 = 69 49 + -14x + x2 = 69 Factor a perfect square on the left side: (x + -7)(x + -7) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + -7) equal to 8.306623863 and -8.306623863.Subproblem 1
x + -7 = 8.306623863 Simplifying x + -7 = 8.306623863 Reorder the terms: -7 + x = 8.306623863 Solving -7 + x = 8.306623863 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 = 8.306623863 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.306623863 + 7 x = 8.306623863 + 7 Combine like terms: 8.306623863 + 7 = 15.306623863 x = 15.306623863 Simplifying x = 15.306623863Subproblem 2
x + -7 = -8.306623863 Simplifying x + -7 = -8.306623863 Reorder the terms: -7 + x = -8.306623863 Solving -7 + x = -8.306623863 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 = -8.306623863 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.306623863 + 7 x = -8.306623863 + 7 Combine like terms: -8.306623863 + 7 = -1.306623863 x = -1.306623863 Simplifying x = -1.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.306623863, -1.306623863}
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