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Simplifying 0.8q2 + 2q + -3 = 0 Reorder the terms: -3 + 2q + 0.8q2 = 0 Solving -3 + 2q + 0.8q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -3.75 + 2.5q + q2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 2.5q + 3.75 + q2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 2.5q + q2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 2.5q + q2 = 0 + 3.75 2.5q + q2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 2.5q + q2 = 3.75 The q term is 2.5q. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5q + 1.5625 + q2 = 3.75 + 1.5625 Reorder the terms: 1.5625 + 2.5q + q2 = 3.75 + 1.5625 Combine like terms: 3.75 + 1.5625 = 5.3125 1.5625 + 2.5q + q2 = 5.3125 Factor a perfect square on the left side: (q + 1.25)(q + 1.25) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (q + 1.25) equal to 2.304886114 and -2.304886114.Subproblem 1
q + 1.25 = 2.304886114 Simplifying q + 1.25 = 2.304886114 Reorder the terms: 1.25 + q = 2.304886114 Solving 1.25 + q = 2.304886114 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + q = 2.304886114 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + q = 2.304886114 + -1.25 q = 2.304886114 + -1.25 Combine like terms: 2.304886114 + -1.25 = 1.054886114 q = 1.054886114 Simplifying q = 1.054886114Subproblem 2
q + 1.25 = -2.304886114 Simplifying q + 1.25 = -2.304886114 Reorder the terms: 1.25 + q = -2.304886114 Solving 1.25 + q = -2.304886114 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + q = -2.304886114 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + q = -2.304886114 + -1.25 q = -2.304886114 + -1.25 Combine like terms: -2.304886114 + -1.25 = -3.554886114 q = -3.554886114 Simplifying q = -3.554886114Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.054886114, -3.554886114}
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