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Simplifying 0.0079x2 + 0.057x = 629.5 + -0.54x2 Reorder the terms: 0.057x + 0.0079x2 = 629.5 + -0.54x2 Solving 0.057x + 0.0079x2 = 629.5 + -0.54x2 Solving for variable 'x'. Reorder the terms: -629.5 + 0.057x + 0.0079x2 + 0.54x2 = 629.5 + -0.54x2 + -629.5 + 0.54x2 Combine like terms: 0.0079x2 + 0.54x2 = 0.5479x2 -629.5 + 0.057x + 0.5479x2 = 629.5 + -0.54x2 + -629.5 + 0.54x2 Reorder the terms: -629.5 + 0.057x + 0.5479x2 = 629.5 + -629.5 + -0.54x2 + 0.54x2 Combine like terms: 629.5 + -629.5 = 0.0 -629.5 + 0.057x + 0.5479x2 = 0.0 + -0.54x2 + 0.54x2 -629.5 + 0.057x + 0.5479x2 = -0.54x2 + 0.54x2 Combine like terms: -0.54x2 + 0.54x2 = 0.00 -629.5 + 0.057x + 0.5479x2 = 0.00 Begin completing the square. Divide all terms by 0.5479 the coefficient of the squared term: Divide each side by '0.5479'. -1148.932287 + 0.1040335828x + x2 = 0 Move the constant term to the right: Add '1148.932287' to each side of the equation. -1148.932287 + 0.1040335828x + 1148.932287 + x2 = 0 + 1148.932287 Reorder the terms: -1148.932287 + 1148.932287 + 0.1040335828x + x2 = 0 + 1148.932287 Combine like terms: -1148.932287 + 1148.932287 = 0.000000 0.000000 + 0.1040335828x + x2 = 0 + 1148.932287 0.1040335828x + x2 = 0 + 1148.932287 Combine like terms: 0 + 1148.932287 = 1148.932287 0.1040335828x + x2 = 1148.932287 The x term is 0.1040335828x. Take half its coefficient (0.0520167914). Square it (0.002705746588) and add it to both sides. Add '0.002705746588' to each side of the equation. 0.1040335828x + 0.002705746588 + x2 = 1148.932287 + 0.002705746588 Reorder the terms: 0.002705746588 + 0.1040335828x + x2 = 1148.932287 + 0.002705746588 Combine like terms: 1148.932287 + 0.002705746588 = 1148.934992746588 0.002705746588 + 0.1040335828x + x2 = 1148.934992746588 Factor a perfect square on the left side: (x + 0.0520167914)(x + 0.0520167914) = 1148.934992746588 Calculate the square root of the right side: 33.895943603 Break this problem into two subproblems by setting (x + 0.0520167914) equal to 33.895943603 and -33.895943603.Subproblem 1
x + 0.0520167914 = 33.895943603 Simplifying x + 0.0520167914 = 33.895943603 Reorder the terms: 0.0520167914 + x = 33.895943603 Solving 0.0520167914 + x = 33.895943603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0520167914' to each side of the equation. 0.0520167914 + -0.0520167914 + x = 33.895943603 + -0.0520167914 Combine like terms: 0.0520167914 + -0.0520167914 = 0.0000000000 0.0000000000 + x = 33.895943603 + -0.0520167914 x = 33.895943603 + -0.0520167914 Combine like terms: 33.895943603 + -0.0520167914 = 33.8439268116 x = 33.8439268116 Simplifying x = 33.8439268116Subproblem 2
x + 0.0520167914 = -33.895943603 Simplifying x + 0.0520167914 = -33.895943603 Reorder the terms: 0.0520167914 + x = -33.895943603 Solving 0.0520167914 + x = -33.895943603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0520167914' to each side of the equation. 0.0520167914 + -0.0520167914 + x = -33.895943603 + -0.0520167914 Combine like terms: 0.0520167914 + -0.0520167914 = 0.0000000000 0.0000000000 + x = -33.895943603 + -0.0520167914 x = -33.895943603 + -0.0520167914 Combine like terms: -33.895943603 + -0.0520167914 = -33.9479603944 x = -33.9479603944 Simplifying x = -33.9479603944Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.8439268116, -33.9479603944}
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