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Simplifying 976x + -1x2 = 213.495 Solving 976x + -1x2 = 213.495 Solving for variable 'x'. Reorder the terms: -213.495 + 976x + -1x2 = 213.495 + -213.495 Combine like terms: 213.495 + -213.495 = 0.000 -213.495 + 976x + -1x2 = 0.000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 213.495 + -976x + x2 = 0.000 Move the constant term to the right: Add '-213.495' to each side of the equation. 213.495 + -976x + -213.495 + x2 = 0.000 + -213.495 Reorder the terms: 213.495 + -213.495 + -976x + x2 = 0.000 + -213.495 Combine like terms: 213.495 + -213.495 = 0.000 0.000 + -976x + x2 = 0.000 + -213.495 -976x + x2 = 0.000 + -213.495 Combine like terms: 0.000 + -213.495 = -213.495 -976x + x2 = -213.495 The x term is -976x. Take half its coefficient (-488). Square it (238144) and add it to both sides. Add '238144' to each side of the equation. -976x + 238144 + x2 = -213.495 + 238144 Reorder the terms: 238144 + -976x + x2 = -213.495 + 238144 Combine like terms: -213.495 + 238144 = 237930.505 238144 + -976x + x2 = 237930.505 Factor a perfect square on the left side: (x + -488)(x + -488) = 237930.505 Calculate the square root of the right side: 487.781206075 Break this problem into two subproblems by setting (x + -488) equal to 487.781206075 and -487.781206075.Subproblem 1
x + -488 = 487.781206075 Simplifying x + -488 = 487.781206075 Reorder the terms: -488 + x = 487.781206075 Solving -488 + x = 487.781206075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '488' to each side of the equation. -488 + 488 + x = 487.781206075 + 488 Combine like terms: -488 + 488 = 0 0 + x = 487.781206075 + 488 x = 487.781206075 + 488 Combine like terms: 487.781206075 + 488 = 975.781206075 x = 975.781206075 Simplifying x = 975.781206075Subproblem 2
x + -488 = -487.781206075 Simplifying x + -488 = -487.781206075 Reorder the terms: -488 + x = -487.781206075 Solving -488 + x = -487.781206075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '488' to each side of the equation. -488 + 488 + x = -487.781206075 + 488 Combine like terms: -488 + 488 = 0 0 + x = -487.781206075 + 488 x = -487.781206075 + 488 Combine like terms: -487.781206075 + 488 = 0.218793925 x = 0.218793925 Simplifying x = 0.218793925Solution
The solution to the problem is based on the solutions from the subproblems. x = {975.781206075, 0.218793925}
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