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Simplifying 0 = 1500 + 75x + -0.2x2 Solving 0 = 1500 + 75x + -0.2x2 Solving for variable 'x'. Combine like terms: 0 + -1500 = -1500 -1500 + -75x + 0.2x2 = 1500 + 75x + -0.2x2 + -1500 + -75x + 0.2x2 Reorder the terms: -1500 + -75x + 0.2x2 = 1500 + -1500 + 75x + -75x + -0.2x2 + 0.2x2 Combine like terms: 1500 + -1500 = 0 -1500 + -75x + 0.2x2 = 0 + 75x + -75x + -0.2x2 + 0.2x2 -1500 + -75x + 0.2x2 = 75x + -75x + -0.2x2 + 0.2x2 Combine like terms: 75x + -75x = 0 -1500 + -75x + 0.2x2 = 0 + -0.2x2 + 0.2x2 -1500 + -75x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 -1500 + -75x + 0.2x2 = 0.0 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 = 42656.25 35156.25 + -375x + x2 = 42656.25 Factor a perfect square on the left side: (x + -187.5)(x + -187.5) = 42656.25 Calculate the square root of the right side: 206.533895523 Break this problem into two subproblems by setting (x + -187.5) equal to 206.533895523 and -206.533895523.Subproblem 1
x + -187.5 = 206.533895523 Simplifying x + -187.5 = 206.533895523 Reorder the terms: -187.5 + x = 206.533895523 Solving -187.5 + x = 206.533895523 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 = 206.533895523 + 187.5 Combine like terms: -187.5 + 187.5 = 0.0 0.0 + x = 206.533895523 + 187.5 x = 206.533895523 + 187.5 Combine like terms: 206.533895523 + 187.5 = 394.033895523 x = 394.033895523 Simplifying x = 394.033895523Subproblem 2
x + -187.5 = -206.533895523 Simplifying x + -187.5 = -206.533895523 Reorder the terms: -187.5 + x = -206.533895523 Solving -187.5 + x = -206.533895523 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 = -206.533895523 + 187.5 Combine like terms: -187.5 + 187.5 = 0.0 0.0 + x = -206.533895523 + 187.5 x = -206.533895523 + 187.5 Combine like terms: -206.533895523 + 187.5 = -19.033895523 x = -19.033895523 Simplifying x = -19.033895523Solution
The solution to the problem is based on the solutions from the subproblems. x = {394.033895523, -19.033895523}
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