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Simplifying 8.16x2 + 3.22x = 4.69 Reorder the terms: 3.22x + 8.16x2 = 4.69 Solving 3.22x + 8.16x2 = 4.69 Solving for variable 'x'. Reorder the terms: -4.69 + 3.22x + 8.16x2 = 4.69 + -4.69 Combine like terms: 4.69 + -4.69 = 0.00 -4.69 + 3.22x + 8.16x2 = 0.00 Begin completing the square. Divide all terms by 8.16 the coefficient of the squared term: Divide each side by '8.16'. -0.574754902 + 0.3946078431x + x2 = 0 Move the constant term to the right: Add '0.574754902' to each side of the equation. -0.574754902 + 0.3946078431x + 0.574754902 + x2 = 0 + 0.574754902 Reorder the terms: -0.574754902 + 0.574754902 + 0.3946078431x + x2 = 0 + 0.574754902 Combine like terms: -0.574754902 + 0.574754902 = 0.000000000 0.000000000 + 0.3946078431x + x2 = 0 + 0.574754902 0.3946078431x + x2 = 0 + 0.574754902 Combine like terms: 0 + 0.574754902 = 0.574754902 0.3946078431x + x2 = 0.574754902 The x term is 0.3946078431x. Take half its coefficient (0.1973039216). Square it (0.03892883748) and add it to both sides. Add '0.03892883748' to each side of the equation. 0.3946078431x + 0.03892883748 + x2 = 0.574754902 + 0.03892883748 Reorder the terms: 0.03892883748 + 0.3946078431x + x2 = 0.574754902 + 0.03892883748 Combine like terms: 0.574754902 + 0.03892883748 = 0.61368373948 0.03892883748 + 0.3946078431x + x2 = 0.61368373948 Factor a perfect square on the left side: (x + 0.1973039216)(x + 0.1973039216) = 0.61368373948 Calculate the square root of the right side: 0.78337969 Break this problem into two subproblems by setting (x + 0.1973039216) equal to 0.78337969 and -0.78337969.Subproblem 1
x + 0.1973039216 = 0.78337969 Simplifying x + 0.1973039216 = 0.78337969 Reorder the terms: 0.1973039216 + x = 0.78337969 Solving 0.1973039216 + x = 0.78337969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1973039216' to each side of the equation. 0.1973039216 + -0.1973039216 + x = 0.78337969 + -0.1973039216 Combine like terms: 0.1973039216 + -0.1973039216 = 0.0000000000 0.0000000000 + x = 0.78337969 + -0.1973039216 x = 0.78337969 + -0.1973039216 Combine like terms: 0.78337969 + -0.1973039216 = 0.5860757684 x = 0.5860757684 Simplifying x = 0.5860757684Subproblem 2
x + 0.1973039216 = -0.78337969 Simplifying x + 0.1973039216 = -0.78337969 Reorder the terms: 0.1973039216 + x = -0.78337969 Solving 0.1973039216 + x = -0.78337969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1973039216' to each side of the equation. 0.1973039216 + -0.1973039216 + x = -0.78337969 + -0.1973039216 Combine like terms: 0.1973039216 + -0.1973039216 = 0.0000000000 0.0000000000 + x = -0.78337969 + -0.1973039216 x = -0.78337969 + -0.1973039216 Combine like terms: -0.78337969 + -0.1973039216 = -0.9806836116 x = -0.9806836116 Simplifying x = -0.9806836116Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5860757684, -0.9806836116}
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