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Simplifying 563x + -0.5x2 + -142104 = 0 Reorder the terms: -142104 + 563x + -0.5x2 = 0 Solving -142104 + 563x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 284208 + -1126x + x2 = 0 Move the constant term to the right: Add '-284208' to each side of the equation. 284208 + -1126x + -284208 + x2 = 0 + -284208 Reorder the terms: 284208 + -284208 + -1126x + x2 = 0 + -284208 Combine like terms: 284208 + -284208 = 0 0 + -1126x + x2 = 0 + -284208 -1126x + x2 = 0 + -284208 Combine like terms: 0 + -284208 = -284208 -1126x + x2 = -284208 The x term is -1126x. Take half its coefficient (-563). Square it (316969) and add it to both sides. Add '316969' to each side of the equation. -1126x + 316969 + x2 = -284208 + 316969 Reorder the terms: 316969 + -1126x + x2 = -284208 + 316969 Combine like terms: -284208 + 316969 = 32761 316969 + -1126x + x2 = 32761 Factor a perfect square on the left side: (x + -563)(x + -563) = 32761 Calculate the square root of the right side: 181 Break this problem into two subproblems by setting (x + -563) equal to 181 and -181.Subproblem 1
x + -563 = 181 Simplifying x + -563 = 181 Reorder the terms: -563 + x = 181 Solving -563 + x = 181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '563' to each side of the equation. -563 + 563 + x = 181 + 563 Combine like terms: -563 + 563 = 0 0 + x = 181 + 563 x = 181 + 563 Combine like terms: 181 + 563 = 744 x = 744 Simplifying x = 744Subproblem 2
x + -563 = -181 Simplifying x + -563 = -181 Reorder the terms: -563 + x = -181 Solving -563 + x = -181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '563' to each side of the equation. -563 + 563 + x = -181 + 563 Combine like terms: -563 + 563 = 0 0 + x = -181 + 563 x = -181 + 563 Combine like terms: -181 + 563 = 382 x = 382 Simplifying x = 382Solution
The solution to the problem is based on the solutions from the subproblems. x = {744, 382}
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