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Simplifying -5x + 350 = 0.1x2 + -1x + -5 Reorder the terms: 350 + -5x = 0.1x2 + -1x + -5 Reorder the terms: 350 + -5x = -5 + -1x + 0.1x2 Solving 350 + -5x = -5 + -1x + 0.1x2 Solving for variable 'x'. Reorder the terms: 350 + 5 + -5x + x + -0.1x2 = -5 + -1x + 0.1x2 + 5 + x + -0.1x2 Combine like terms: 350 + 5 = 355 355 + -5x + x + -0.1x2 = -5 + -1x + 0.1x2 + 5 + x + -0.1x2 Combine like terms: -5x + x = -4x 355 + -4x + -0.1x2 = -5 + -1x + 0.1x2 + 5 + x + -0.1x2 Reorder the terms: 355 + -4x + -0.1x2 = -5 + 5 + -1x + x + 0.1x2 + -0.1x2 Combine like terms: -5 + 5 = 0 355 + -4x + -0.1x2 = 0 + -1x + x + 0.1x2 + -0.1x2 355 + -4x + -0.1x2 = -1x + x + 0.1x2 + -0.1x2 Combine like terms: -1x + x = 0 355 + -4x + -0.1x2 = 0 + 0.1x2 + -0.1x2 355 + -4x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 355 + -4x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -3550 + 40x + x2 = 0 Move the constant term to the right: Add '3550' to each side of the equation. -3550 + 40x + 3550 + x2 = 0 + 3550 Reorder the terms: -3550 + 3550 + 40x + x2 = 0 + 3550 Combine like terms: -3550 + 3550 = 0 0 + 40x + x2 = 0 + 3550 40x + x2 = 0 + 3550 Combine like terms: 0 + 3550 = 3550 40x + x2 = 3550 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 3550 + 400 Reorder the terms: 400 + 40x + x2 = 3550 + 400 Combine like terms: 3550 + 400 = 3950 400 + 40x + x2 = 3950 Factor a perfect square on the left side: (x + 20)(x + 20) = 3950 Calculate the square root of the right side: 62.84902545 Break this problem into two subproblems by setting (x + 20) equal to 62.84902545 and -62.84902545.Subproblem 1
x + 20 = 62.84902545 Simplifying x + 20 = 62.84902545 Reorder the terms: 20 + x = 62.84902545 Solving 20 + x = 62.84902545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 62.84902545 + -20 Combine like terms: 20 + -20 = 0 0 + x = 62.84902545 + -20 x = 62.84902545 + -20 Combine like terms: 62.84902545 + -20 = 42.84902545 x = 42.84902545 Simplifying x = 42.84902545Subproblem 2
x + 20 = -62.84902545 Simplifying x + 20 = -62.84902545 Reorder the terms: 20 + x = -62.84902545 Solving 20 + x = -62.84902545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -62.84902545 + -20 Combine like terms: 20 + -20 = 0 0 + x = -62.84902545 + -20 x = -62.84902545 + -20 Combine like terms: -62.84902545 + -20 = -82.84902545 x = -82.84902545 Simplifying x = -82.84902545Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.84902545, -82.84902545}
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