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Simplifying 0 = -0.3x2 + 75x + -2000 Reorder the terms: 0 = -2000 + 75x + -0.3x2 Solving 0 = -2000 + 75x + -0.3x2 Solving for variable 'x'. Combine like terms: 0 + 2000 = 2000 2000 + -75x + 0.3x2 = -2000 + 75x + -0.3x2 + 2000 + -75x + 0.3x2 Reorder the terms: 2000 + -75x + 0.3x2 = -2000 + 2000 + 75x + -75x + -0.3x2 + 0.3x2 Combine like terms: -2000 + 2000 = 0 2000 + -75x + 0.3x2 = 0 + 75x + -75x + -0.3x2 + 0.3x2 2000 + -75x + 0.3x2 = 75x + -75x + -0.3x2 + 0.3x2 Combine like terms: 75x + -75x = 0 2000 + -75x + 0.3x2 = 0 + -0.3x2 + 0.3x2 2000 + -75x + 0.3x2 = -0.3x2 + 0.3x2 Combine like terms: -0.3x2 + 0.3x2 = 0.0 2000 + -75x + 0.3x2 = 0.0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 6666.666667 + -250x + x2 = 0 Move the constant term to the right: Add '-6666.666667' to each side of the equation. 6666.666667 + -250x + -6666.666667 + x2 = 0 + -6666.666667 Reorder the terms: 6666.666667 + -6666.666667 + -250x + x2 = 0 + -6666.666667 Combine like terms: 6666.666667 + -6666.666667 = 0.000000 0.000000 + -250x + x2 = 0 + -6666.666667 -250x + x2 = 0 + -6666.666667 Combine like terms: 0 + -6666.666667 = -6666.666667 -250x + x2 = -6666.666667 The x term is -250x. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250x + 15625 + x2 = -6666.666667 + 15625 Reorder the terms: 15625 + -250x + x2 = -6666.666667 + 15625 Combine like terms: -6666.666667 + 15625 = 8958.333333 15625 + -250x + x2 = 8958.333333 Factor a perfect square on the left side: (x + -125)(x + -125) = 8958.333333 Calculate the square root of the right side: 94.648472428 Break this problem into two subproblems by setting (x + -125) equal to 94.648472428 and -94.648472428.Subproblem 1
x + -125 = 94.648472428 Simplifying x + -125 = 94.648472428 Reorder the terms: -125 + x = 94.648472428 Solving -125 + x = 94.648472428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 94.648472428 + 125 Combine like terms: -125 + 125 = 0 0 + x = 94.648472428 + 125 x = 94.648472428 + 125 Combine like terms: 94.648472428 + 125 = 219.648472428 x = 219.648472428 Simplifying x = 219.648472428Subproblem 2
x + -125 = -94.648472428 Simplifying x + -125 = -94.648472428 Reorder the terms: -125 + x = -94.648472428 Solving -125 + x = -94.648472428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -94.648472428 + 125 Combine like terms: -125 + 125 = 0 0 + x = -94.648472428 + 125 x = -94.648472428 + 125 Combine like terms: -94.648472428 + 125 = 30.351527572 x = 30.351527572 Simplifying x = 30.351527572Solution
The solution to the problem is based on the solutions from the subproblems. x = {219.648472428, 30.351527572}
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