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Simplifying 7x + -0.01x2 = 0.005 Solving 7x + -0.01x2 = 0.005 Solving for variable 'x'. Reorder the terms: -0.005 + 7x + -0.01x2 = 0.005 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 -0.005 + 7x + -0.01x2 = 0.000 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 0.5 + -700x + x2 = 0.0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -700x + -0.5 + x2 = 0.0 + -0.5 Reorder the terms: 0.5 + -0.5 + -700x + x2 = 0.0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -700x + x2 = 0.0 + -0.5 -700x + x2 = 0.0 + -0.5 Combine like terms: 0.0 + -0.5 = -0.5 -700x + x2 = -0.5 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 = -0.5 + 122500 Reorder the terms: 122500 + -700x + x2 = -0.5 + 122500 Combine like terms: -0.5 + 122500 = 122499.5 122500 + -700x + x2 = 122499.5 Factor a perfect square on the left side: (x + -350)(x + -350) = 122499.5 Calculate the square root of the right side: 349.999285714 Break this problem into two subproblems by setting (x + -350) equal to 349.999285714 and -349.999285714.Subproblem 1
x + -350 = 349.999285714 Simplifying x + -350 = 349.999285714 Reorder the terms: -350 + x = 349.999285714 Solving -350 + x = 349.999285714 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 = 349.999285714 + 350 Combine like terms: -350 + 350 = 0 0 + x = 349.999285714 + 350 x = 349.999285714 + 350 Combine like terms: 349.999285714 + 350 = 699.999285714 x = 699.999285714 Simplifying x = 699.999285714Subproblem 2
x + -350 = -349.999285714 Simplifying x + -350 = -349.999285714 Reorder the terms: -350 + x = -349.999285714 Solving -350 + x = -349.999285714 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 = -349.999285714 + 350 Combine like terms: -350 + 350 = 0 0 + x = -349.999285714 + 350 x = -349.999285714 + 350 Combine like terms: -349.999285714 + 350 = 0.000714286 x = 0.000714286 Simplifying x = 0.000714286Solution
The solution to the problem is based on the solutions from the subproblems. x = {699.999285714, 0.000714286}
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