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Simplifying 13x2 + -2900x = 210000 Reorder the terms: -2900x + 13x2 = 210000 Solving -2900x + 13x2 = 210000 Solving for variable 'x'. Reorder the terms: -210000 + -2900x + 13x2 = 210000 + -210000 Combine like terms: 210000 + -210000 = 0 -210000 + -2900x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -16153.84615 + -223.0769231x + x2 = 0 Move the constant term to the right: Add '16153.84615' to each side of the equation. -16153.84615 + -223.0769231x + 16153.84615 + x2 = 0 + 16153.84615 Reorder the terms: -16153.84615 + 16153.84615 + -223.0769231x + x2 = 0 + 16153.84615 Combine like terms: -16153.84615 + 16153.84615 = 0.00000 0.00000 + -223.0769231x + x2 = 0 + 16153.84615 -223.0769231x + x2 = 0 + 16153.84615 Combine like terms: 0 + 16153.84615 = 16153.84615 -223.0769231x + x2 = 16153.84615 The x term is -223.0769231x. Take half its coefficient (-111.5384616). Square it (12440.82842) and add it to both sides. Add '12440.82842' to each side of the equation. -223.0769231x + 12440.82842 + x2 = 16153.84615 + 12440.82842 Reorder the terms: 12440.82842 + -223.0769231x + x2 = 16153.84615 + 12440.82842 Combine like terms: 16153.84615 + 12440.82842 = 28594.67457 12440.82842 + -223.0769231x + x2 = 28594.67457 Factor a perfect square on the left side: (x + -111.5384616)(x + -111.5384616) = 28594.67457 Calculate the square root of the right side: 169.099599556 Break this problem into two subproblems by setting (x + -111.5384616) equal to 169.099599556 and -169.099599556.Subproblem 1
x + -111.5384616 = 169.099599556 Simplifying x + -111.5384616 = 169.099599556 Reorder the terms: -111.5384616 + x = 169.099599556 Solving -111.5384616 + x = 169.099599556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '111.5384616' to each side of the equation. -111.5384616 + 111.5384616 + x = 169.099599556 + 111.5384616 Combine like terms: -111.5384616 + 111.5384616 = 0.0000000 0.0000000 + x = 169.099599556 + 111.5384616 x = 169.099599556 + 111.5384616 Combine like terms: 169.099599556 + 111.5384616 = 280.638061156 x = 280.638061156 Simplifying x = 280.638061156Subproblem 2
x + -111.5384616 = -169.099599556 Simplifying x + -111.5384616 = -169.099599556 Reorder the terms: -111.5384616 + x = -169.099599556 Solving -111.5384616 + x = -169.099599556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '111.5384616' to each side of the equation. -111.5384616 + 111.5384616 + x = -169.099599556 + 111.5384616 Combine like terms: -111.5384616 + 111.5384616 = 0.0000000 0.0000000 + x = -169.099599556 + 111.5384616 x = -169.099599556 + 111.5384616 Combine like terms: -169.099599556 + 111.5384616 = -57.561137956 x = -57.561137956 Simplifying x = -57.561137956Solution
The solution to the problem is based on the solutions from the subproblems. x = {280.638061156, -57.561137956}
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