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Simplifying 0.01x2 + -28x + 18700 = 0 Reorder the terms: 18700 + -28x + 0.01x2 = 0 Solving 18700 + -28x + 0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 1870000 + -2800x + x2 = 0 Move the constant term to the right: Add '-1870000' to each side of the equation. 1870000 + -2800x + -1870000 + x2 = 0 + -1870000 Reorder the terms: 1870000 + -1870000 + -2800x + x2 = 0 + -1870000 Combine like terms: 1870000 + -1870000 = 0 0 + -2800x + x2 = 0 + -1870000 -2800x + x2 = 0 + -1870000 Combine like terms: 0 + -1870000 = -1870000 -2800x + x2 = -1870000 The x term is -2800x. Take half its coefficient (-1400). Square it (1960000) and add it to both sides. Add '1960000' to each side of the equation. -2800x + 1960000 + x2 = -1870000 + 1960000 Reorder the terms: 1960000 + -2800x + x2 = -1870000 + 1960000 Combine like terms: -1870000 + 1960000 = 90000 1960000 + -2800x + x2 = 90000 Factor a perfect square on the left side: (x + -1400)(x + -1400) = 90000 Calculate the square root of the right side: 300 Break this problem into two subproblems by setting (x + -1400) equal to 300 and -300.Subproblem 1
x + -1400 = 300 Simplifying x + -1400 = 300 Reorder the terms: -1400 + x = 300 Solving -1400 + x = 300 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1400' to each side of the equation. -1400 + 1400 + x = 300 + 1400 Combine like terms: -1400 + 1400 = 0 0 + x = 300 + 1400 x = 300 + 1400 Combine like terms: 300 + 1400 = 1700 x = 1700 Simplifying x = 1700Subproblem 2
x + -1400 = -300 Simplifying x + -1400 = -300 Reorder the terms: -1400 + x = -300 Solving -1400 + x = -300 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1400' to each side of the equation. -1400 + 1400 + x = -300 + 1400 Combine like terms: -1400 + 1400 = 0 0 + x = -300 + 1400 x = -300 + 1400 Combine like terms: -300 + 1400 = 1100 x = 1100 Simplifying x = 1100Solution
The solution to the problem is based on the solutions from the subproblems. x = {1700, 1100}
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