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Simplifying x2 + -112x + -344 = 0 Reorder the terms: -344 + -112x + x2 = 0 Solving -344 + -112x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '344' to each side of the equation. -344 + -112x + 344 + x2 = 0 + 344 Reorder the terms: -344 + 344 + -112x + x2 = 0 + 344 Combine like terms: -344 + 344 = 0 0 + -112x + x2 = 0 + 344 -112x + x2 = 0 + 344 Combine like terms: 0 + 344 = 344 -112x + x2 = 344 The x term is -112x. Take half its coefficient (-56). Square it (3136) and add it to both sides. Add '3136' to each side of the equation. -112x + 3136 + x2 = 344 + 3136 Reorder the terms: 3136 + -112x + x2 = 344 + 3136 Combine like terms: 344 + 3136 = 3480 3136 + -112x + x2 = 3480 Factor a perfect square on the left side: (x + -56)(x + -56) = 3480 Calculate the square root of the right side: 58.991524815 Break this problem into two subproblems by setting (x + -56) equal to 58.991524815 and -58.991524815.Subproblem 1
x + -56 = 58.991524815 Simplifying x + -56 = 58.991524815 Reorder the terms: -56 + x = 58.991524815 Solving -56 + x = 58.991524815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + x = 58.991524815 + 56 Combine like terms: -56 + 56 = 0 0 + x = 58.991524815 + 56 x = 58.991524815 + 56 Combine like terms: 58.991524815 + 56 = 114.991524815 x = 114.991524815 Simplifying x = 114.991524815Subproblem 2
x + -56 = -58.991524815 Simplifying x + -56 = -58.991524815 Reorder the terms: -56 + x = -58.991524815 Solving -56 + x = -58.991524815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + x = -58.991524815 + 56 Combine like terms: -56 + 56 = 0 0 + x = -58.991524815 + 56 x = -58.991524815 + 56 Combine like terms: -58.991524815 + 56 = -2.991524815 x = -2.991524815 Simplifying x = -2.991524815Solution
The solution to the problem is based on the solutions from the subproblems. x = {114.991524815, -2.991524815}
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