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Simplifying 0 = 196 + 53x + -1x2 Solving 0 = 196 + 53x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -196 = -196 -196 + -53x + x2 = 196 + 53x + -1x2 + -196 + -53x + x2 Reorder the terms: -196 + -53x + x2 = 196 + -196 + 53x + -53x + -1x2 + x2 Combine like terms: 196 + -196 = 0 -196 + -53x + x2 = 0 + 53x + -53x + -1x2 + x2 -196 + -53x + x2 = 53x + -53x + -1x2 + x2 Combine like terms: 53x + -53x = 0 -196 + -53x + x2 = 0 + -1x2 + x2 -196 + -53x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -196 + -53x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + -53x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + -53x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + -53x + x2 = 0 + 196 -53x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 -53x + x2 = 196 The x term is -53x. Take half its coefficient (-26.5). Square it (702.25) and add it to both sides. Add '702.25' to each side of the equation. -53x + 702.25 + x2 = 196 + 702.25 Reorder the terms: 702.25 + -53x + x2 = 196 + 702.25 Combine like terms: 196 + 702.25 = 898.25 702.25 + -53x + x2 = 898.25 Factor a perfect square on the left side: (x + -26.5)(x + -26.5) = 898.25 Calculate the square root of the right side: 29.970819141 Break this problem into two subproblems by setting (x + -26.5) equal to 29.970819141 and -29.970819141.Subproblem 1
x + -26.5 = 29.970819141 Simplifying x + -26.5 = 29.970819141 Reorder the terms: -26.5 + x = 29.970819141 Solving -26.5 + x = 29.970819141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.5' to each side of the equation. -26.5 + 26.5 + x = 29.970819141 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = 29.970819141 + 26.5 x = 29.970819141 + 26.5 Combine like terms: 29.970819141 + 26.5 = 56.470819141 x = 56.470819141 Simplifying x = 56.470819141Subproblem 2
x + -26.5 = -29.970819141 Simplifying x + -26.5 = -29.970819141 Reorder the terms: -26.5 + x = -29.970819141 Solving -26.5 + x = -29.970819141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.5' to each side of the equation. -26.5 + 26.5 + x = -29.970819141 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + x = -29.970819141 + 26.5 x = -29.970819141 + 26.5 Combine like terms: -29.970819141 + 26.5 = -3.470819141 x = -3.470819141 Simplifying x = -3.470819141Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.470819141, -3.470819141}
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