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Simplifying 312.5x2 + -50x + 2 = 0 Reorder the terms: 2 + -50x + 312.5x2 = 0 Solving 2 + -50x + 312.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 312.5 the coefficient of the squared term: Divide each side by '312.5'. 0.0064 + -0.16x + x2 = 0 Move the constant term to the right: Add '-0.0064' to each side of the equation. 0.0064 + -0.16x + -0.0064 + x2 = 0 + -0.0064 Reorder the terms: 0.0064 + -0.0064 + -0.16x + x2 = 0 + -0.0064 Combine like terms: 0.0064 + -0.0064 = 0.0000 0.0000 + -0.16x + x2 = 0 + -0.0064 -0.16x + x2 = 0 + -0.0064 Combine like terms: 0 + -0.0064 = -0.0064 -0.16x + x2 = -0.0064 The x term is -0.16x. Take half its coefficient (-0.08). Square it (0.0064) and add it to both sides. Add '0.0064' to each side of the equation. -0.16x + 0.0064 + x2 = -0.0064 + 0.0064 Reorder the terms: 0.0064 + -0.16x + x2 = -0.0064 + 0.0064 Combine like terms: -0.0064 + 0.0064 = 0.0000 0.0064 + -0.16x + x2 = 0.0000 Factor a perfect square on the left side: (x + -0.08)(x + -0.08) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + -0.08) equal to 0.0000 and 0.0000.Subproblem 1
x + -0.08 = 0.0000 Simplifying x + -0.08 = 0.0000 Reorder the terms: -0.08 + x = 0.0000 Solving -0.08 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08' to each side of the equation. -0.08 + 0.08 + x = 0.0000 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + x = 0.0000 + 0.08 x = 0.0000 + 0.08 Combine like terms: 0.0000 + 0.08 = 0.08 x = 0.08 Simplifying x = 0.08Subproblem 2
x + -0.08 = 0.0000 Simplifying x + -0.08 = 0.0000 Reorder the terms: -0.08 + x = 0.0000 Solving -0.08 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08' to each side of the equation. -0.08 + 0.08 + x = 0.0000 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + x = 0.0000 + 0.08 x = 0.0000 + 0.08 Combine like terms: 0.0000 + 0.08 = 0.08 x = 0.08 Simplifying x = 0.08Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.08, 0.08}
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