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Simplifying 0.02x2 + -28x + 8400 = 0 Reorder the terms: 8400 + -28x + 0.02x2 = 0 Solving 8400 + -28x + 0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 420000 + -1400x + x2 = 0 Move the constant term to the right: Add '-420000' to each side of the equation. 420000 + -1400x + -420000 + x2 = 0 + -420000 Reorder the terms: 420000 + -420000 + -1400x + x2 = 0 + -420000 Combine like terms: 420000 + -420000 = 0 0 + -1400x + x2 = 0 + -420000 -1400x + x2 = 0 + -420000 Combine like terms: 0 + -420000 = -420000 -1400x + x2 = -420000 The x term is -1400x. Take half its coefficient (-700). Square it (490000) and add it to both sides. Add '490000' to each side of the equation. -1400x + 490000 + x2 = -420000 + 490000 Reorder the terms: 490000 + -1400x + x2 = -420000 + 490000 Combine like terms: -420000 + 490000 = 70000 490000 + -1400x + x2 = 70000 Factor a perfect square on the left side: (x + -700)(x + -700) = 70000 Calculate the square root of the right side: 264.575131106 Break this problem into two subproblems by setting (x + -700) equal to 264.575131106 and -264.575131106.Subproblem 1
x + -700 = 264.575131106 Simplifying x + -700 = 264.575131106 Reorder the terms: -700 + x = 264.575131106 Solving -700 + x = 264.575131106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '700' to each side of the equation. -700 + 700 + x = 264.575131106 + 700 Combine like terms: -700 + 700 = 0 0 + x = 264.575131106 + 700 x = 264.575131106 + 700 Combine like terms: 264.575131106 + 700 = 964.575131106 x = 964.575131106 Simplifying x = 964.575131106Subproblem 2
x + -700 = -264.575131106 Simplifying x + -700 = -264.575131106 Reorder the terms: -700 + x = -264.575131106 Solving -700 + x = -264.575131106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '700' to each side of the equation. -700 + 700 + x = -264.575131106 + 700 Combine like terms: -700 + 700 = 0 0 + x = -264.575131106 + 700 x = -264.575131106 + 700 Combine like terms: -264.575131106 + 700 = 435.424868894 x = 435.424868894 Simplifying x = 435.424868894Solution
The solution to the problem is based on the solutions from the subproblems. x = {964.575131106, 435.424868894}
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