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Simplifying -750x2 + 15000x = -1 Reorder the terms: 15000x + -750x2 = -1 Solving 15000x + -750x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 15000x + -750x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 15000x + -750x2 = 0 Begin completing the square. Divide all terms by -750 the coefficient of the squared term: Divide each side by '-750'. -0.001333333333 + -20x + x2 = 0 Move the constant term to the right: Add '0.001333333333' to each side of the equation. -0.001333333333 + -20x + 0.001333333333 + x2 = 0 + 0.001333333333 Reorder the terms: -0.001333333333 + 0.001333333333 + -20x + x2 = 0 + 0.001333333333 Combine like terms: -0.001333333333 + 0.001333333333 = 0.000000000000 0.000000000000 + -20x + x2 = 0 + 0.001333333333 -20x + x2 = 0 + 0.001333333333 Combine like terms: 0 + 0.001333333333 = 0.001333333333 -20x + x2 = 0.001333333333 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 0.001333333333 + 100 Reorder the terms: 100 + -20x + x2 = 0.001333333333 + 100 Combine like terms: 0.001333333333 + 100 = 100.001333333333 100 + -20x + x2 = 100.001333333333 Factor a perfect square on the left side: (x + -10)(x + -10) = 100.001333333333 Calculate the square root of the right side: 10.000066666 Break this problem into two subproblems by setting (x + -10) equal to 10.000066666 and -10.000066666.Subproblem 1
x + -10 = 10.000066666 Simplifying x + -10 = 10.000066666 Reorder the terms: -10 + x = 10.000066666 Solving -10 + x = 10.000066666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 10.000066666 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.000066666 + 10 x = 10.000066666 + 10 Combine like terms: 10.000066666 + 10 = 20.000066666 x = 20.000066666 Simplifying x = 20.000066666Subproblem 2
x + -10 = -10.000066666 Simplifying x + -10 = -10.000066666 Reorder the terms: -10 + x = -10.000066666 Solving -10 + x = -10.000066666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -10.000066666 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.000066666 + 10 x = -10.000066666 + 10 Combine like terms: -10.000066666 + 10 = -0.000066666 x = -0.000066666 Simplifying x = -0.000066666Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.000066666, -0.000066666}
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