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Simplifying 44213 = 0.62x2 + -0.048x Reorder the terms: 44213 = -0.048x + 0.62x2 Solving 44213 = -0.048x + 0.62x2 Solving for variable 'x'. Reorder the terms: 44213 + 0.048x + -0.62x2 = -0.048x + 0.048x + 0.62x2 + -0.62x2 Combine like terms: -0.048x + 0.048x = 0.000 44213 + 0.048x + -0.62x2 = 0.000 + 0.62x2 + -0.62x2 44213 + 0.048x + -0.62x2 = 0.62x2 + -0.62x2 Combine like terms: 0.62x2 + -0.62x2 = 0.00 44213 + 0.048x + -0.62x2 = 0.00 Begin completing the square. Divide all terms by -0.62 the coefficient of the squared term: Divide each side by '-0.62'. -71311.29032 + -0.07741935484x + x2 = 0 Move the constant term to the right: Add '71311.29032' to each side of the equation. -71311.29032 + -0.07741935484x + 71311.29032 + x2 = 0 + 71311.29032 Reorder the terms: -71311.29032 + 71311.29032 + -0.07741935484x + x2 = 0 + 71311.29032 Combine like terms: -71311.29032 + 71311.29032 = 0.00000 0.00000 + -0.07741935484x + x2 = 0 + 71311.29032 -0.07741935484x + x2 = 0 + 71311.29032 Combine like terms: 0 + 71311.29032 = 71311.29032 -0.07741935484x + x2 = 71311.29032 The x term is -0.07741935484x. Take half its coefficient (-0.03870967742). Square it (0.001498439126) and add it to both sides. Add '0.001498439126' to each side of the equation. -0.07741935484x + 0.001498439126 + x2 = 71311.29032 + 0.001498439126 Reorder the terms: 0.001498439126 + -0.07741935484x + x2 = 71311.29032 + 0.001498439126 Combine like terms: 71311.29032 + 0.001498439126 = 71311.291818439126 0.001498439126 + -0.07741935484x + x2 = 71311.291818439126 Factor a perfect square on the left side: (x + -0.03870967742)(x + -0.03870967742) = 71311.291818439126 Calculate the square root of the right side: 267.041741715 Break this problem into two subproblems by setting (x + -0.03870967742) equal to 267.041741715 and -267.041741715.Subproblem 1
x + -0.03870967742 = 267.041741715 Simplifying x + -0.03870967742 = 267.041741715 Reorder the terms: -0.03870967742 + x = 267.041741715 Solving -0.03870967742 + x = 267.041741715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03870967742' to each side of the equation. -0.03870967742 + 0.03870967742 + x = 267.041741715 + 0.03870967742 Combine like terms: -0.03870967742 + 0.03870967742 = 0.00000000000 0.00000000000 + x = 267.041741715 + 0.03870967742 x = 267.041741715 + 0.03870967742 Combine like terms: 267.041741715 + 0.03870967742 = 267.08045139242 x = 267.08045139242 Simplifying x = 267.08045139242Subproblem 2
x + -0.03870967742 = -267.041741715 Simplifying x + -0.03870967742 = -267.041741715 Reorder the terms: -0.03870967742 + x = -267.041741715 Solving -0.03870967742 + x = -267.041741715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03870967742' to each side of the equation. -0.03870967742 + 0.03870967742 + x = -267.041741715 + 0.03870967742 Combine like terms: -0.03870967742 + 0.03870967742 = 0.00000000000 0.00000000000 + x = -267.041741715 + 0.03870967742 x = -267.041741715 + 0.03870967742 Combine like terms: -267.041741715 + 0.03870967742 = -267.00303203758 x = -267.00303203758 Simplifying x = -267.00303203758Solution
The solution to the problem is based on the solutions from the subproblems. x = {267.08045139242, -267.00303203758}
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