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Simplifying -4q2 + 7q + 4 = 0 Reorder the terms: 4 + 7q + -4q2 = 0 Solving 4 + 7q + -4q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1 + -1.75q + q2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.75q + 1 + q2 = 0 + 1 Reorder the terms: -1 + 1 + -1.75q + q2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.75q + q2 = 0 + 1 -1.75q + q2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.75q + q2 = 1 The q term is -1.75q. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75q + 0.765625 + q2 = 1 + 0.765625 Reorder the terms: 0.765625 + -1.75q + q2 = 1 + 0.765625 Combine like terms: 1 + 0.765625 = 1.765625 0.765625 + -1.75q + q2 = 1.765625 Factor a perfect square on the left side: (q + -0.875)(q + -0.875) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (q + -0.875) equal to 1.328768227 and -1.328768227.Subproblem 1
q + -0.875 = 1.328768227 Simplifying q + -0.875 = 1.328768227 Reorder the terms: -0.875 + q = 1.328768227 Solving -0.875 + q = 1.328768227 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + q = 1.328768227 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + q = 1.328768227 + 0.875 q = 1.328768227 + 0.875 Combine like terms: 1.328768227 + 0.875 = 2.203768227 q = 2.203768227 Simplifying q = 2.203768227Subproblem 2
q + -0.875 = -1.328768227 Simplifying q + -0.875 = -1.328768227 Reorder the terms: -0.875 + q = -1.328768227 Solving -0.875 + q = -1.328768227 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + q = -1.328768227 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + q = -1.328768227 + 0.875 q = -1.328768227 + 0.875 Combine like terms: -1.328768227 + 0.875 = -0.453768227 q = -0.453768227 Simplifying q = -0.453768227Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.203768227, -0.453768227}
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