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Simplifying 0 = 0.0001x2 + 0.07x + -1.6 Reorder the terms: 0 = -1.6 + 0.07x + 0.0001x2 Solving 0 = -1.6 + 0.07x + 0.0001x2 Solving for variable 'x'. Combine like terms: 0 + 1.6 = 1.6 1.6 + -0.07x + -0.0001x2 = -1.6 + 0.07x + 0.0001x2 + 1.6 + -0.07x + -0.0001x2 Reorder the terms: 1.6 + -0.07x + -0.0001x2 = -1.6 + 1.6 + 0.07x + -0.07x + 0.0001x2 + -0.0001x2 Combine like terms: -1.6 + 1.6 = 0.0 1.6 + -0.07x + -0.0001x2 = 0.0 + 0.07x + -0.07x + 0.0001x2 + -0.0001x2 1.6 + -0.07x + -0.0001x2 = 0.07x + -0.07x + 0.0001x2 + -0.0001x2 Combine like terms: 0.07x + -0.07x = 0.00 1.6 + -0.07x + -0.0001x2 = 0.00 + 0.0001x2 + -0.0001x2 1.6 + -0.07x + -0.0001x2 = 0.0001x2 + -0.0001x2 Combine like terms: 0.0001x2 + -0.0001x2 = 0.0000 1.6 + -0.07x + -0.0001x2 = 0.0000 Begin completing the square. Divide all terms by -0.0001 the coefficient of the squared term: Divide each side by '-0.0001'. -16000 + 700x + x2 = 0 Move the constant term to the right: Add '16000' to each side of the equation. -16000 + 700x + 16000 + x2 = 0 + 16000 Reorder the terms: -16000 + 16000 + 700x + x2 = 0 + 16000 Combine like terms: -16000 + 16000 = 0 0 + 700x + x2 = 0 + 16000 700x + x2 = 0 + 16000 Combine like terms: 0 + 16000 = 16000 700x + x2 = 16000 The x term is 700x. Take half its coefficient (350). Square it (122500) and add it to both sides. Add '122500' to each side of the equation. 700x + 122500 + x2 = 16000 + 122500 Reorder the terms: 122500 + 700x + x2 = 16000 + 122500 Combine like terms: 16000 + 122500 = 138500 122500 + 700x + x2 = 138500 Factor a perfect square on the left side: (x + 350)(x + 350) = 138500 Calculate the square root of the right side: 372.155881319 Break this problem into two subproblems by setting (x + 350) equal to 372.155881319 and -372.155881319.Subproblem 1
x + 350 = 372.155881319 Simplifying x + 350 = 372.155881319 Reorder the terms: 350 + x = 372.155881319 Solving 350 + x = 372.155881319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + x = 372.155881319 + -350 Combine like terms: 350 + -350 = 0 0 + x = 372.155881319 + -350 x = 372.155881319 + -350 Combine like terms: 372.155881319 + -350 = 22.155881319 x = 22.155881319 Simplifying x = 22.155881319Subproblem 2
x + 350 = -372.155881319 Simplifying x + 350 = -372.155881319 Reorder the terms: 350 + x = -372.155881319 Solving 350 + x = -372.155881319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + x = -372.155881319 + -350 Combine like terms: 350 + -350 = 0 0 + x = -372.155881319 + -350 x = -372.155881319 + -350 Combine like terms: -372.155881319 + -350 = -722.155881319 x = -722.155881319 Simplifying x = -722.155881319Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.155881319, -722.155881319}
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