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Simplifying -0.003x2 + 0.34x + 23 = 0 Reorder the terms: 23 + 0.34x + -0.003x2 = 0 Solving 23 + 0.34x + -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'. -7666.666667 + -113.3333333x + x2 = 0 Move the constant term to the right: Add '7666.666667' to each side of the equation. -7666.666667 + -113.3333333x + 7666.666667 + x2 = 0 + 7666.666667 Reorder the terms: -7666.666667 + 7666.666667 + -113.3333333x + x2 = 0 + 7666.666667 Combine like terms: -7666.666667 + 7666.666667 = 0.000000 0.000000 + -113.3333333x + x2 = 0 + 7666.666667 -113.3333333x + x2 = 0 + 7666.666667 Combine like terms: 0 + 7666.666667 = 7666.666667 -113.3333333x + x2 = 7666.666667 The x term is -113.3333333x. Take half its coefficient (-56.66666665). Square it (3211.111109) and add it to both sides. Add '3211.111109' to each side of the equation. -113.3333333x + 3211.111109 + x2 = 7666.666667 + 3211.111109 Reorder the terms: 3211.111109 + -113.3333333x + x2 = 7666.666667 + 3211.111109 Combine like terms: 7666.666667 + 3211.111109 = 10877.777776 3211.111109 + -113.3333333x + x2 = 10877.777776 Factor a perfect square on the left side: (x + -56.66666665)(x + -56.66666665) = 10877.777776 Calculate the square root of the right side: 104.296585639 Break this problem into two subproblems by setting (x + -56.66666665) equal to 104.296585639 and -104.296585639.Subproblem 1
x + -56.66666665 = 104.296585639 Simplifying x + -56.66666665 = 104.296585639 Reorder the terms: -56.66666665 + x = 104.296585639 Solving -56.66666665 + x = 104.296585639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56.66666665' to each side of the equation. -56.66666665 + 56.66666665 + x = 104.296585639 + 56.66666665 Combine like terms: -56.66666665 + 56.66666665 = 0.00000000 0.00000000 + x = 104.296585639 + 56.66666665 x = 104.296585639 + 56.66666665 Combine like terms: 104.296585639 + 56.66666665 = 160.963252289 x = 160.963252289 Simplifying x = 160.963252289Subproblem 2
x + -56.66666665 = -104.296585639 Simplifying x + -56.66666665 = -104.296585639 Reorder the terms: -56.66666665 + x = -104.296585639 Solving -56.66666665 + x = -104.296585639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56.66666665' to each side of the equation. -56.66666665 + 56.66666665 + x = -104.296585639 + 56.66666665 Combine like terms: -56.66666665 + 56.66666665 = 0.00000000 0.00000000 + x = -104.296585639 + 56.66666665 x = -104.296585639 + 56.66666665 Combine like terms: -104.296585639 + 56.66666665 = -47.629918989 x = -47.629918989 Simplifying x = -47.629918989Solution
The solution to the problem is based on the solutions from the subproblems. x = {160.963252289, -47.629918989}
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