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Simplifying 0(x) = 0.3x2 + 75x + -2000 Anything times zero is zero. 0x = 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 = 22291.666667 15625 + 250x + x2 = 22291.666667 Factor a perfect square on the left side: (x + 125)(x + 125) = 22291.666667 Calculate the square root of the right side: 149.303940561 Break this problem into two subproblems by setting (x + 125) equal to 149.303940561 and -149.303940561.Subproblem 1
x + 125 = 149.303940561 Simplifying x + 125 = 149.303940561 Reorder the terms: 125 + x = 149.303940561 Solving 125 + x = 149.303940561 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 = 149.303940561 + -125 Combine like terms: 125 + -125 = 0 0 + x = 149.303940561 + -125 x = 149.303940561 + -125 Combine like terms: 149.303940561 + -125 = 24.303940561 x = 24.303940561 Simplifying x = 24.303940561Subproblem 2
x + 125 = -149.303940561 Simplifying x + 125 = -149.303940561 Reorder the terms: 125 + x = -149.303940561 Solving 125 + x = -149.303940561 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 = -149.303940561 + -125 Combine like terms: 125 + -125 = 0 0 + x = -149.303940561 + -125 x = -149.303940561 + -125 Combine like terms: -149.303940561 + -125 = -274.303940561 x = -274.303940561 Simplifying x = -274.303940561Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.303940561, -274.303940561}
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