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Simplifying 0 = -0.06x2 + 10.1x + 5 Reorder the terms: 0 = 5 + 10.1x + -0.06x2 Solving 0 = 5 + 10.1x + -0.06x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -10.1x + 0.06x2 = 5 + 10.1x + -0.06x2 + -5 + -10.1x + 0.06x2 Reorder the terms: -5 + -10.1x + 0.06x2 = 5 + -5 + 10.1x + -10.1x + -0.06x2 + 0.06x2 Combine like terms: 5 + -5 = 0 -5 + -10.1x + 0.06x2 = 0 + 10.1x + -10.1x + -0.06x2 + 0.06x2 -5 + -10.1x + 0.06x2 = 10.1x + -10.1x + -0.06x2 + 0.06x2 Combine like terms: 10.1x + -10.1x = 0.0 -5 + -10.1x + 0.06x2 = 0.0 + -0.06x2 + 0.06x2 -5 + -10.1x + 0.06x2 = -0.06x2 + 0.06x2 Combine like terms: -0.06x2 + 0.06x2 = 0.00 -5 + -10.1x + 0.06x2 = 0.00 Begin completing the square. Divide all terms by 0.06 the coefficient of the squared term: Divide each side by '0.06'. -83.33333333 + -168.3333333x + x2 = 0 Move the constant term to the right: Add '83.33333333' to each side of the equation. -83.33333333 + -168.3333333x + 83.33333333 + x2 = 0 + 83.33333333 Reorder the terms: -83.33333333 + 83.33333333 + -168.3333333x + x2 = 0 + 83.33333333 Combine like terms: -83.33333333 + 83.33333333 = 0.00000000 0.00000000 + -168.3333333x + x2 = 0 + 83.33333333 -168.3333333x + x2 = 0 + 83.33333333 Combine like terms: 0 + 83.33333333 = 83.33333333 -168.3333333x + x2 = 83.33333333 The x term is -168.3333333x. Take half its coefficient (-84.16666665). Square it (7084.027775) and add it to both sides. Add '7084.027775' to each side of the equation. -168.3333333x + 7084.027775 + x2 = 83.33333333 + 7084.027775 Reorder the terms: 7084.027775 + -168.3333333x + x2 = 83.33333333 + 7084.027775 Combine like terms: 83.33333333 + 7084.027775 = 7167.36110833 7084.027775 + -168.3333333x + x2 = 7167.36110833 Factor a perfect square on the left side: (x + -84.16666665)(x + -84.16666665) = 7167.36110833 Calculate the square root of the right side: 84.660268771 Break this problem into two subproblems by setting (x + -84.16666665) equal to 84.660268771 and -84.660268771.Subproblem 1
x + -84.16666665 = 84.660268771 Simplifying x + -84.16666665 = 84.660268771 Reorder the terms: -84.16666665 + x = 84.660268771 Solving -84.16666665 + x = 84.660268771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '84.16666665' to each side of the equation. -84.16666665 + 84.16666665 + x = 84.660268771 + 84.16666665 Combine like terms: -84.16666665 + 84.16666665 = 0.00000000 0.00000000 + x = 84.660268771 + 84.16666665 x = 84.660268771 + 84.16666665 Combine like terms: 84.660268771 + 84.16666665 = 168.826935421 x = 168.826935421 Simplifying x = 168.826935421Subproblem 2
x + -84.16666665 = -84.660268771 Simplifying x + -84.16666665 = -84.660268771 Reorder the terms: -84.16666665 + x = -84.660268771 Solving -84.16666665 + x = -84.660268771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '84.16666665' to each side of the equation. -84.16666665 + 84.16666665 + x = -84.660268771 + 84.16666665 Combine like terms: -84.16666665 + 84.16666665 = 0.00000000 0.00000000 + x = -84.660268771 + 84.16666665 x = -84.660268771 + 84.16666665 Combine like terms: -84.660268771 + 84.16666665 = -0.493602121 x = -0.493602121 Simplifying x = -0.493602121Solution
The solution to the problem is based on the solutions from the subproblems. x = {168.826935421, -0.493602121}
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