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Simplifying 0.3214x2 + -4.6571x = 30.6 Reorder the terms: -4.6571x + 0.3214x2 = 30.6 Solving -4.6571x + 0.3214x2 = 30.6 Solving for variable 'x'. Reorder the terms: -30.6 + -4.6571x + 0.3214x2 = 30.6 + -30.6 Combine like terms: 30.6 + -30.6 = 0.0 -30.6 + -4.6571x + 0.3214x2 = 0.0 Begin completing the square. Divide all terms by 0.3214 the coefficient of the squared term: Divide each side by '0.3214'. -95.20846297 + -14.49004356x + x2 = 0 Move the constant term to the right: Add '95.20846297' to each side of the equation. -95.20846297 + -14.49004356x + 95.20846297 + x2 = 0 + 95.20846297 Reorder the terms: -95.20846297 + 95.20846297 + -14.49004356x + x2 = 0 + 95.20846297 Combine like terms: -95.20846297 + 95.20846297 = 0.00000000 0.00000000 + -14.49004356x + x2 = 0 + 95.20846297 -14.49004356x + x2 = 0 + 95.20846297 Combine like terms: 0 + 95.20846297 = 95.20846297 -14.49004356x + x2 = 95.20846297 The x term is -14.49004356x. Take half its coefficient (-7.24502178). Square it (52.49034059) and add it to both sides. Add '52.49034059' to each side of the equation. -14.49004356x + 52.49034059 + x2 = 95.20846297 + 52.49034059 Reorder the terms: 52.49034059 + -14.49004356x + x2 = 95.20846297 + 52.49034059 Combine like terms: 95.20846297 + 52.49034059 = 147.69880356 52.49034059 + -14.49004356x + x2 = 147.69880356 Factor a perfect square on the left side: (x + -7.24502178)(x + -7.24502178) = 147.69880356 Calculate the square root of the right side: 12.153139659 Break this problem into two subproblems by setting (x + -7.24502178) equal to 12.153139659 and -12.153139659.Subproblem 1
x + -7.24502178 = 12.153139659 Simplifying x + -7.24502178 = 12.153139659 Reorder the terms: -7.24502178 + x = 12.153139659 Solving -7.24502178 + x = 12.153139659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.24502178' to each side of the equation. -7.24502178 + 7.24502178 + x = 12.153139659 + 7.24502178 Combine like terms: -7.24502178 + 7.24502178 = 0.00000000 0.00000000 + x = 12.153139659 + 7.24502178 x = 12.153139659 + 7.24502178 Combine like terms: 12.153139659 + 7.24502178 = 19.398161439 x = 19.398161439 Simplifying x = 19.398161439Subproblem 2
x + -7.24502178 = -12.153139659 Simplifying x + -7.24502178 = -12.153139659 Reorder the terms: -7.24502178 + x = -12.153139659 Solving -7.24502178 + x = -12.153139659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.24502178' to each side of the equation. -7.24502178 + 7.24502178 + x = -12.153139659 + 7.24502178 Combine like terms: -7.24502178 + 7.24502178 = 0.00000000 0.00000000 + x = -12.153139659 + 7.24502178 x = -12.153139659 + 7.24502178 Combine like terms: -12.153139659 + 7.24502178 = -4.908117879 x = -4.908117879 Simplifying x = -4.908117879Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.398161439, -4.908117879}
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