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Simplifying x2 + -14x + 31 = 61 Reorder the terms: 31 + -14x + x2 = 61 Solving 31 + -14x + x2 = 61 Solving for variable 'x'. Reorder the terms: 31 + -61 + -14x + x2 = 61 + -61 Combine like terms: 31 + -61 = -30 -30 + -14x + x2 = 61 + -61 Combine like terms: 61 + -61 = 0 -30 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -14x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -14x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -14x + x2 = 0 + 30 -14x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -14x + x2 = 30 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 = 30 + 49 Reorder the terms: 49 + -14x + x2 = 30 + 49 Combine like terms: 30 + 49 = 79 49 + -14x + x2 = 79 Factor a perfect square on the left side: (x + -7)(x + -7) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + -7) equal to 8.888194417 and -8.888194417.Subproblem 1
x + -7 = 8.888194417 Simplifying x + -7 = 8.888194417 Reorder the terms: -7 + x = 8.888194417 Solving -7 + x = 8.888194417 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 = 8.888194417 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.888194417 + 7 x = 8.888194417 + 7 Combine like terms: 8.888194417 + 7 = 15.888194417 x = 15.888194417 Simplifying x = 15.888194417Subproblem 2
x + -7 = -8.888194417 Simplifying x + -7 = -8.888194417 Reorder the terms: -7 + x = -8.888194417 Solving -7 + x = -8.888194417 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 = -8.888194417 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.888194417 + 7 x = -8.888194417 + 7 Combine like terms: -8.888194417 + 7 = -1.888194417 x = -1.888194417 Simplifying x = -1.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.888194417, -1.888194417}
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