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Simplifying -0.00001x2 + 0.007x + -0.6 = 0 Reorder the terms: -0.6 + 0.007x + -0.00001x2 = 0 Solving -0.6 + 0.007x + -0.00001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.00001 the coefficient of the squared term: Divide each side by '-0.00001'. 60000 + -700x + x2 = 0 Move the constant term to the right: Add '-60000' to each side of the equation. 60000 + -700x + -60000 + x2 = 0 + -60000 Reorder the terms: 60000 + -60000 + -700x + x2 = 0 + -60000 Combine like terms: 60000 + -60000 = 0 0 + -700x + x2 = 0 + -60000 -700x + x2 = 0 + -60000 Combine like terms: 0 + -60000 = -60000 -700x + x2 = -60000 The x term is -700x. Take half its coefficient (-350). Square it (122500) and add it to both sides. Add '122500' to each side of the equation. -700x + 122500 + x2 = -60000 + 122500 Reorder the terms: 122500 + -700x + x2 = -60000 + 122500 Combine like terms: -60000 + 122500 = 62500 122500 + -700x + x2 = 62500 Factor a perfect square on the left side: (x + -350)(x + -350) = 62500 Calculate the square root of the right side: 250 Break this problem into two subproblems by setting (x + -350) equal to 250 and -250.Subproblem 1
x + -350 = 250 Simplifying x + -350 = 250 Reorder the terms: -350 + x = 250 Solving -350 + x = 250 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '350' to each side of the equation. -350 + 350 + x = 250 + 350 Combine like terms: -350 + 350 = 0 0 + x = 250 + 350 x = 250 + 350 Combine like terms: 250 + 350 = 600 x = 600 Simplifying x = 600Subproblem 2
x + -350 = -250 Simplifying x + -350 = -250 Reorder the terms: -350 + x = -250 Solving -350 + x = -250 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '350' to each side of the equation. -350 + 350 + x = -250 + 350 Combine like terms: -350 + 350 = 0 0 + x = -250 + 350 x = -250 + 350 Combine like terms: -250 + 350 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {600, 100}
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