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Simplifying 224x + -1x2 = 784 Solving 224x + -1x2 = 784 Solving for variable 'x'. Reorder the terms: -784 + 224x + -1x2 = 784 + -784 Combine like terms: 784 + -784 = 0 -784 + 224x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 784 + -224x + x2 = 0 Move the constant term to the right: Add '-784' to each side of the equation. 784 + -224x + -784 + x2 = 0 + -784 Reorder the terms: 784 + -784 + -224x + x2 = 0 + -784 Combine like terms: 784 + -784 = 0 0 + -224x + x2 = 0 + -784 -224x + x2 = 0 + -784 Combine like terms: 0 + -784 = -784 -224x + x2 = -784 The x term is -224x. Take half its coefficient (-112). Square it (12544) and add it to both sides. Add '12544' to each side of the equation. -224x + 12544 + x2 = -784 + 12544 Reorder the terms: 12544 + -224x + x2 = -784 + 12544 Combine like terms: -784 + 12544 = 11760 12544 + -224x + x2 = 11760 Factor a perfect square on the left side: (x + -112)(x + -112) = 11760 Calculate the square root of the right side: 108.443533694 Break this problem into two subproblems by setting (x + -112) equal to 108.443533694 and -108.443533694.Subproblem 1
x + -112 = 108.443533694 Simplifying x + -112 = 108.443533694 Reorder the terms: -112 + x = 108.443533694 Solving -112 + x = 108.443533694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '112' to each side of the equation. -112 + 112 + x = 108.443533694 + 112 Combine like terms: -112 + 112 = 0 0 + x = 108.443533694 + 112 x = 108.443533694 + 112 Combine like terms: 108.443533694 + 112 = 220.443533694 x = 220.443533694 Simplifying x = 220.443533694Subproblem 2
x + -112 = -108.443533694 Simplifying x + -112 = -108.443533694 Reorder the terms: -112 + x = -108.443533694 Solving -112 + x = -108.443533694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '112' to each side of the equation. -112 + 112 + x = -108.443533694 + 112 Combine like terms: -112 + 112 = 0 0 + x = -108.443533694 + 112 x = -108.443533694 + 112 Combine like terms: -108.443533694 + 112 = 3.556466306 x = 3.556466306 Simplifying x = 3.556466306Solution
The solution to the problem is based on the solutions from the subproblems. x = {220.443533694, 3.556466306}
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