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Simplifying x2 + -14x + -8332 = 0 Reorder the terms: -8332 + -14x + x2 = 0 Solving -8332 + -14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8332' to each side of the equation. -8332 + -14x + 8332 + x2 = 0 + 8332 Reorder the terms: -8332 + 8332 + -14x + x2 = 0 + 8332 Combine like terms: -8332 + 8332 = 0 0 + -14x + x2 = 0 + 8332 -14x + x2 = 0 + 8332 Combine like terms: 0 + 8332 = 8332 -14x + x2 = 8332 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 = 8332 + 49 Reorder the terms: 49 + -14x + x2 = 8332 + 49 Combine like terms: 8332 + 49 = 8381 49 + -14x + x2 = 8381 Factor a perfect square on the left side: (x + -7)(x + -7) = 8381 Calculate the square root of the right side: 91.547801721 Break this problem into two subproblems by setting (x + -7) equal to 91.547801721 and -91.547801721.Subproblem 1
x + -7 = 91.547801721 Simplifying x + -7 = 91.547801721 Reorder the terms: -7 + x = 91.547801721 Solving -7 + x = 91.547801721 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 = 91.547801721 + 7 Combine like terms: -7 + 7 = 0 0 + x = 91.547801721 + 7 x = 91.547801721 + 7 Combine like terms: 91.547801721 + 7 = 98.547801721 x = 98.547801721 Simplifying x = 98.547801721Subproblem 2
x + -7 = -91.547801721 Simplifying x + -7 = -91.547801721 Reorder the terms: -7 + x = -91.547801721 Solving -7 + x = -91.547801721 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 = -91.547801721 + 7 Combine like terms: -7 + 7 = 0 0 + x = -91.547801721 + 7 x = -91.547801721 + 7 Combine like terms: -91.547801721 + 7 = -84.547801721 x = -84.547801721 Simplifying x = -84.547801721Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.547801721, -84.547801721}
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