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Simplifying -16x2 + 93x + 211 = 0 Reorder the terms: 211 + 93x + -16x2 = 0 Solving 211 + 93x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -13.1875 + -5.8125x + x2 = 0 Move the constant term to the right: Add '13.1875' to each side of the equation. -13.1875 + -5.8125x + 13.1875 + x2 = 0 + 13.1875 Reorder the terms: -13.1875 + 13.1875 + -5.8125x + x2 = 0 + 13.1875 Combine like terms: -13.1875 + 13.1875 = 0.0000 0.0000 + -5.8125x + x2 = 0 + 13.1875 -5.8125x + x2 = 0 + 13.1875 Combine like terms: 0 + 13.1875 = 13.1875 -5.8125x + x2 = 13.1875 The x term is -5.8125x. Take half its coefficient (-2.90625). Square it (8.446289063) and add it to both sides. Add '8.446289063' to each side of the equation. -5.8125x + 8.446289063 + x2 = 13.1875 + 8.446289063 Reorder the terms: 8.446289063 + -5.8125x + x2 = 13.1875 + 8.446289063 Combine like terms: 13.1875 + 8.446289063 = 21.633789063 8.446289063 + -5.8125x + x2 = 21.633789063 Factor a perfect square on the left side: (x + -2.90625)(x + -2.90625) = 21.633789063 Calculate the square root of the right side: 4.651213719 Break this problem into two subproblems by setting (x + -2.90625) equal to 4.651213719 and -4.651213719.Subproblem 1
x + -2.90625 = 4.651213719 Simplifying x + -2.90625 = 4.651213719 Reorder the terms: -2.90625 + x = 4.651213719 Solving -2.90625 + x = 4.651213719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.90625' to each side of the equation. -2.90625 + 2.90625 + x = 4.651213719 + 2.90625 Combine like terms: -2.90625 + 2.90625 = 0.00000 0.00000 + x = 4.651213719 + 2.90625 x = 4.651213719 + 2.90625 Combine like terms: 4.651213719 + 2.90625 = 7.557463719 x = 7.557463719 Simplifying x = 7.557463719Subproblem 2
x + -2.90625 = -4.651213719 Simplifying x + -2.90625 = -4.651213719 Reorder the terms: -2.90625 + x = -4.651213719 Solving -2.90625 + x = -4.651213719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.90625' to each side of the equation. -2.90625 + 2.90625 + x = -4.651213719 + 2.90625 Combine like terms: -2.90625 + 2.90625 = 0.00000 0.00000 + x = -4.651213719 + 2.90625 x = -4.651213719 + 2.90625 Combine like terms: -4.651213719 + 2.90625 = -1.744963719 x = -1.744963719 Simplifying x = -1.744963719Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.557463719, -1.744963719}
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