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Simplifying -0.003x2 + 0.577x + 2 = 0 Reorder the terms: 2 + 0.577x + -0.003x2 = 0 Solving 2 + 0.577x + -0.003x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.003 the coefficient of the squared term: Divide each side by '-0.003'. -666.6666667 + -192.3333333x + x2 = 0 Move the constant term to the right: Add '666.6666667' to each side of the equation. -666.6666667 + -192.3333333x + 666.6666667 + x2 = 0 + 666.6666667 Reorder the terms: -666.6666667 + 666.6666667 + -192.3333333x + x2 = 0 + 666.6666667 Combine like terms: -666.6666667 + 666.6666667 = 0.0000000 0.0000000 + -192.3333333x + x2 = 0 + 666.6666667 -192.3333333x + x2 = 0 + 666.6666667 Combine like terms: 0 + 666.6666667 = 666.6666667 -192.3333333x + x2 = 666.6666667 The x term is -192.3333333x. Take half its coefficient (-96.16666665). Square it (9248.027775) and add it to both sides. Add '9248.027775' to each side of the equation. -192.3333333x + 9248.027775 + x2 = 666.6666667 + 9248.027775 Reorder the terms: 9248.027775 + -192.3333333x + x2 = 666.6666667 + 9248.027775 Combine like terms: 666.6666667 + 9248.027775 = 9914.6944417 9248.027775 + -192.3333333x + x2 = 9914.6944417 Factor a perfect square on the left side: (x + -96.16666665)(x + -96.16666665) = 9914.6944417 Calculate the square root of the right side: 99.572558678 Break this problem into two subproblems by setting (x + -96.16666665) equal to 99.572558678 and -99.572558678.Subproblem 1
x + -96.16666665 = 99.572558678 Simplifying x + -96.16666665 = 99.572558678 Reorder the terms: -96.16666665 + x = 99.572558678 Solving -96.16666665 + x = 99.572558678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '96.16666665' to each side of the equation. -96.16666665 + 96.16666665 + x = 99.572558678 + 96.16666665 Combine like terms: -96.16666665 + 96.16666665 = 0.00000000 0.00000000 + x = 99.572558678 + 96.16666665 x = 99.572558678 + 96.16666665 Combine like terms: 99.572558678 + 96.16666665 = 195.739225328 x = 195.739225328 Simplifying x = 195.739225328Subproblem 2
x + -96.16666665 = -99.572558678 Simplifying x + -96.16666665 = -99.572558678 Reorder the terms: -96.16666665 + x = -99.572558678 Solving -96.16666665 + x = -99.572558678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '96.16666665' to each side of the equation. -96.16666665 + 96.16666665 + x = -99.572558678 + 96.16666665 Combine like terms: -96.16666665 + 96.16666665 = 0.00000000 0.00000000 + x = -99.572558678 + 96.16666665 x = -99.572558678 + 96.16666665 Combine like terms: -99.572558678 + 96.16666665 = -3.405892028 x = -3.405892028 Simplifying x = -3.405892028Solution
The solution to the problem is based on the solutions from the subproblems. x = {195.739225328, -3.405892028}
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