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Simplifying 4q2 + -7q + -90 = 0 Reorder the terms: -90 + -7q + 4q2 = 0 Solving -90 + -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'. -22.5 + -1.75q + q2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -1.75q + 22.5 + q2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -1.75q + q2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -1.75q + q2 = 0 + 22.5 -1.75q + q2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -1.75q + q2 = 22.5 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 = 22.5 + 0.765625 Reorder the terms: 0.765625 + -1.75q + q2 = 22.5 + 0.765625 Combine like terms: 22.5 + 0.765625 = 23.265625 0.765625 + -1.75q + q2 = 23.265625 Factor a perfect square on the left side: (q + -0.875)(q + -0.875) = 23.265625 Calculate the square root of the right side: 4.823445345 Break this problem into two subproblems by setting (q + -0.875) equal to 4.823445345 and -4.823445345.Subproblem 1
q + -0.875 = 4.823445345 Simplifying q + -0.875 = 4.823445345 Reorder the terms: -0.875 + q = 4.823445345 Solving -0.875 + q = 4.823445345 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 = 4.823445345 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + q = 4.823445345 + 0.875 q = 4.823445345 + 0.875 Combine like terms: 4.823445345 + 0.875 = 5.698445345 q = 5.698445345 Simplifying q = 5.698445345Subproblem 2
q + -0.875 = -4.823445345 Simplifying q + -0.875 = -4.823445345 Reorder the terms: -0.875 + q = -4.823445345 Solving -0.875 + q = -4.823445345 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 = -4.823445345 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + q = -4.823445345 + 0.875 q = -4.823445345 + 0.875 Combine like terms: -4.823445345 + 0.875 = -3.948445345 q = -3.948445345 Simplifying q = -3.948445345Solution
The solution to the problem is based on the solutions from the subproblems. q = {5.698445345, -3.948445345}
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