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Simplifying 10x2 + -44x + -635 = 0 Reorder the terms: -635 + -44x + 10x2 = 0 Solving -635 + -44x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -63.5 + -4.4x + x2 = 0 Move the constant term to the right: Add '63.5' to each side of the equation. -63.5 + -4.4x + 63.5 + x2 = 0 + 63.5 Reorder the terms: -63.5 + 63.5 + -4.4x + x2 = 0 + 63.5 Combine like terms: -63.5 + 63.5 = 0.0 0.0 + -4.4x + x2 = 0 + 63.5 -4.4x + x2 = 0 + 63.5 Combine like terms: 0 + 63.5 = 63.5 -4.4x + x2 = 63.5 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = 63.5 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = 63.5 + 4.84 Combine like terms: 63.5 + 4.84 = 68.34 4.84 + -4.4x + x2 = 68.34 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 68.34 Calculate the square root of the right side: 8.266801074 Break this problem into two subproblems by setting (x + -2.2) equal to 8.266801074 and -8.266801074.Subproblem 1
x + -2.2 = 8.266801074 Simplifying x + -2.2 = 8.266801074 Reorder the terms: -2.2 + x = 8.266801074 Solving -2.2 + x = 8.266801074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 8.266801074 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 8.266801074 + 2.2 x = 8.266801074 + 2.2 Combine like terms: 8.266801074 + 2.2 = 10.466801074 x = 10.466801074 Simplifying x = 10.466801074Subproblem 2
x + -2.2 = -8.266801074 Simplifying x + -2.2 = -8.266801074 Reorder the terms: -2.2 + x = -8.266801074 Solving -2.2 + x = -8.266801074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -8.266801074 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -8.266801074 + 2.2 x = -8.266801074 + 2.2 Combine like terms: -8.266801074 + 2.2 = -6.066801074 x = -6.066801074 Simplifying x = -6.066801074Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.466801074, -6.066801074}
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