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Simplifying -3.2x2 + -3.9x + 7.2 = 0 Reorder the terms: 7.2 + -3.9x + -3.2x2 = 0 Solving 7.2 + -3.9x + -3.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.2 the coefficient of the squared term: Divide each side by '-3.2'. -2.25 + 1.21875x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 1.21875x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 1.21875x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 1.21875x + x2 = 0 + 2.25 1.21875x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 1.21875x + x2 = 2.25 The x term is 1.21875x. Take half its coefficient (0.609375). Square it (0.3713378906) and add it to both sides. Add '0.3713378906' to each side of the equation. 1.21875x + 0.3713378906 + x2 = 2.25 + 0.3713378906 Reorder the terms: 0.3713378906 + 1.21875x + x2 = 2.25 + 0.3713378906 Combine like terms: 2.25 + 0.3713378906 = 2.6213378906 0.3713378906 + 1.21875x + x2 = 2.6213378906 Factor a perfect square on the left side: (x + 0.609375)(x + 0.609375) = 2.6213378906 Calculate the square root of the right side: 1.619054629 Break this problem into two subproblems by setting (x + 0.609375) equal to 1.619054629 and -1.619054629.Subproblem 1
x + 0.609375 = 1.619054629 Simplifying x + 0.609375 = 1.619054629 Reorder the terms: 0.609375 + x = 1.619054629 Solving 0.609375 + x = 1.619054629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.609375' to each side of the equation. 0.609375 + -0.609375 + x = 1.619054629 + -0.609375 Combine like terms: 0.609375 + -0.609375 = 0.000000 0.000000 + x = 1.619054629 + -0.609375 x = 1.619054629 + -0.609375 Combine like terms: 1.619054629 + -0.609375 = 1.009679629 x = 1.009679629 Simplifying x = 1.009679629Subproblem 2
x + 0.609375 = -1.619054629 Simplifying x + 0.609375 = -1.619054629 Reorder the terms: 0.609375 + x = -1.619054629 Solving 0.609375 + x = -1.619054629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.609375' to each side of the equation. 0.609375 + -0.609375 + x = -1.619054629 + -0.609375 Combine like terms: 0.609375 + -0.609375 = 0.000000 0.000000 + x = -1.619054629 + -0.609375 x = -1.619054629 + -0.609375 Combine like terms: -1.619054629 + -0.609375 = -2.228429629 x = -2.228429629 Simplifying x = -2.228429629Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.009679629, -2.228429629}
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