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Simplifying 0.2x2 + -75x + 1500 = 0 Reorder the terms: 1500 + -75x + 0.2x2 = 0 Solving 1500 + -75x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 7500 + -375x + x2 = 0 Move the constant term to the right: Add '-7500' to each side of the equation. 7500 + -375x + -7500 + x2 = 0 + -7500 Reorder the terms: 7500 + -7500 + -375x + x2 = 0 + -7500 Combine like terms: 7500 + -7500 = 0 0 + -375x + x2 = 0 + -7500 -375x + x2 = 0 + -7500 Combine like terms: 0 + -7500 = -7500 -375x + x2 = -7500 The x term is -375x. Take half its coefficient (-187.5). Square it (35156.25) and add it to both sides. Add '35156.25' to each side of the equation. -375x + 35156.25 + x2 = -7500 + 35156.25 Reorder the terms: 35156.25 + -375x + x2 = -7500 + 35156.25 Combine like terms: -7500 + 35156.25 = 27656.25 35156.25 + -375x + x2 = 27656.25 Factor a perfect square on the left side: (x + -187.5)(x + -187.5) = 27656.25 Calculate the square root of the right side: 166.301683696 Break this problem into two subproblems by setting (x + -187.5) equal to 166.301683696 and -166.301683696.Subproblem 1
x + -187.5 = 166.301683696 Simplifying x + -187.5 = 166.301683696 Reorder the terms: -187.5 + x = 166.301683696 Solving -187.5 + x = 166.301683696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '187.5' to each side of the equation. -187.5 + 187.5 + x = 166.301683696 + 187.5 Combine like terms: -187.5 + 187.5 = 0.0 0.0 + x = 166.301683696 + 187.5 x = 166.301683696 + 187.5 Combine like terms: 166.301683696 + 187.5 = 353.801683696 x = 353.801683696 Simplifying x = 353.801683696Subproblem 2
x + -187.5 = -166.301683696 Simplifying x + -187.5 = -166.301683696 Reorder the terms: -187.5 + x = -166.301683696 Solving -187.5 + x = -166.301683696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '187.5' to each side of the equation. -187.5 + 187.5 + x = -166.301683696 + 187.5 Combine like terms: -187.5 + 187.5 = 0.0 0.0 + x = -166.301683696 + 187.5 x = -166.301683696 + 187.5 Combine like terms: -166.301683696 + 187.5 = 21.198316304 x = 21.198316304 Simplifying x = 21.198316304Solution
The solution to the problem is based on the solutions from the subproblems. x = {353.801683696, 21.198316304}
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