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Simplifying x2 + 699x + -0.00418 = 0 Reorder the terms: -0.00418 + 699x + x2 = 0 Solving -0.00418 + 699x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.00418' to each side of the equation. -0.00418 + 699x + 0.00418 + x2 = 0 + 0.00418 Reorder the terms: -0.00418 + 0.00418 + 699x + x2 = 0 + 0.00418 Combine like terms: -0.00418 + 0.00418 = 0.00000 0.00000 + 699x + x2 = 0 + 0.00418 699x + x2 = 0 + 0.00418 Combine like terms: 0 + 0.00418 = 0.00418 699x + x2 = 0.00418 The x term is 699x. Take half its coefficient (349.5). Square it (122150.25) and add it to both sides. Add '122150.25' to each side of the equation. 699x + 122150.25 + x2 = 0.00418 + 122150.25 Reorder the terms: 122150.25 + 699x + x2 = 0.00418 + 122150.25 Combine like terms: 0.00418 + 122150.25 = 122150.25418 122150.25 + 699x + x2 = 122150.25418 Factor a perfect square on the left side: (x + 349.5)(x + 349.5) = 122150.25418 Calculate the square root of the right side: 349.50000598 Break this problem into two subproblems by setting (x + 349.5) equal to 349.50000598 and -349.50000598.Subproblem 1
x + 349.5 = 349.50000598 Simplifying x + 349.5 = 349.50000598 Reorder the terms: 349.5 + x = 349.50000598 Solving 349.5 + x = 349.50000598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-349.5' to each side of the equation. 349.5 + -349.5 + x = 349.50000598 + -349.5 Combine like terms: 349.5 + -349.5 = 0.0 0.0 + x = 349.50000598 + -349.5 x = 349.50000598 + -349.5 Combine like terms: 349.50000598 + -349.5 = 0.00000598 x = 0.00000598 Simplifying x = 0.00000598Subproblem 2
x + 349.5 = -349.50000598 Simplifying x + 349.5 = -349.50000598 Reorder the terms: 349.5 + x = -349.50000598 Solving 349.5 + x = -349.50000598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-349.5' to each side of the equation. 349.5 + -349.5 + x = -349.50000598 + -349.5 Combine like terms: 349.5 + -349.5 = 0.0 0.0 + x = -349.50000598 + -349.5 x = -349.50000598 + -349.5 Combine like terms: -349.50000598 + -349.5 = -699.00000598 x = -699.00000598 Simplifying x = -699.00000598Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00000598, -699.00000598}
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