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Simplifying -0.084x2 + 0.839x + 5 = 0 Reorder the terms: 5 + 0.839x + -0.084x2 = 0 Solving 5 + 0.839x + -0.084x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.084 the coefficient of the squared term: Divide each side by '-0.084'. -59.52380952 + -9.988095238x + x2 = 0 Move the constant term to the right: Add '59.52380952' to each side of the equation. -59.52380952 + -9.988095238x + 59.52380952 + x2 = 0 + 59.52380952 Reorder the terms: -59.52380952 + 59.52380952 + -9.988095238x + x2 = 0 + 59.52380952 Combine like terms: -59.52380952 + 59.52380952 = 0.00000000 0.00000000 + -9.988095238x + x2 = 0 + 59.52380952 -9.988095238x + x2 = 0 + 59.52380952 Combine like terms: 0 + 59.52380952 = 59.52380952 -9.988095238x + x2 = 59.52380952 The x term is -9.988095238x. Take half its coefficient (-4.994047619). Square it (24.94051162) and add it to both sides. Add '24.94051162' to each side of the equation. -9.988095238x + 24.94051162 + x2 = 59.52380952 + 24.94051162 Reorder the terms: 24.94051162 + -9.988095238x + x2 = 59.52380952 + 24.94051162 Combine like terms: 59.52380952 + 24.94051162 = 84.46432114 24.94051162 + -9.988095238x + x2 = 84.46432114 Factor a perfect square on the left side: (x + -4.994047619)(x + -4.994047619) = 84.46432114 Calculate the square root of the right side: 9.190447276 Break this problem into two subproblems by setting (x + -4.994047619) equal to 9.190447276 and -9.190447276.Subproblem 1
x + -4.994047619 = 9.190447276 Simplifying x + -4.994047619 = 9.190447276 Reorder the terms: -4.994047619 + x = 9.190447276 Solving -4.994047619 + x = 9.190447276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.994047619' to each side of the equation. -4.994047619 + 4.994047619 + x = 9.190447276 + 4.994047619 Combine like terms: -4.994047619 + 4.994047619 = 0.000000000 0.000000000 + x = 9.190447276 + 4.994047619 x = 9.190447276 + 4.994047619 Combine like terms: 9.190447276 + 4.994047619 = 14.184494895 x = 14.184494895 Simplifying x = 14.184494895Subproblem 2
x + -4.994047619 = -9.190447276 Simplifying x + -4.994047619 = -9.190447276 Reorder the terms: -4.994047619 + x = -9.190447276 Solving -4.994047619 + x = -9.190447276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.994047619' to each side of the equation. -4.994047619 + 4.994047619 + x = -9.190447276 + 4.994047619 Combine like terms: -4.994047619 + 4.994047619 = 0.000000000 0.000000000 + x = -9.190447276 + 4.994047619 x = -9.190447276 + 4.994047619 Combine like terms: -9.190447276 + 4.994047619 = -4.196399657 x = -4.196399657 Simplifying x = -4.196399657Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.184494895, -4.196399657}
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