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Simplifying 7.7x2 + -34.8x + 34.8 = 0 Reorder the terms: 34.8 + -34.8x + 7.7x2 = 0 Solving 34.8 + -34.8x + 7.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7.7 the coefficient of the squared term: Divide each side by '7.7'. 4.519480519 + -4.519480519x + x2 = 0 Move the constant term to the right: Add '-4.519480519' to each side of the equation. 4.519480519 + -4.519480519x + -4.519480519 + x2 = 0 + -4.519480519 Reorder the terms: 4.519480519 + -4.519480519 + -4.519480519x + x2 = 0 + -4.519480519 Combine like terms: 4.519480519 + -4.519480519 = 0.000000000 0.000000000 + -4.519480519x + x2 = 0 + -4.519480519 -4.519480519x + x2 = 0 + -4.519480519 Combine like terms: 0 + -4.519480519 = -4.519480519 -4.519480519x + x2 = -4.519480519 The x term is -4.519480519x. Take half its coefficient (-2.25974026). Square it (5.106426043) and add it to both sides. Add '5.106426043' to each side of the equation. -4.519480519x + 5.106426043 + x2 = -4.519480519 + 5.106426043 Reorder the terms: 5.106426043 + -4.519480519x + x2 = -4.519480519 + 5.106426043 Combine like terms: -4.519480519 + 5.106426043 = 0.586945524 5.106426043 + -4.519480519x + x2 = 0.586945524 Factor a perfect square on the left side: (x + -2.25974026)(x + -2.25974026) = 0.586945524 Calculate the square root of the right side: 0.7661237 Break this problem into two subproblems by setting (x + -2.25974026) equal to 0.7661237 and -0.7661237.Subproblem 1
x + -2.25974026 = 0.7661237 Simplifying x + -2.25974026 = 0.7661237 Reorder the terms: -2.25974026 + x = 0.7661237 Solving -2.25974026 + x = 0.7661237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25974026' to each side of the equation. -2.25974026 + 2.25974026 + x = 0.7661237 + 2.25974026 Combine like terms: -2.25974026 + 2.25974026 = 0.00000000 0.00000000 + x = 0.7661237 + 2.25974026 x = 0.7661237 + 2.25974026 Combine like terms: 0.7661237 + 2.25974026 = 3.02586396 x = 3.02586396 Simplifying x = 3.02586396Subproblem 2
x + -2.25974026 = -0.7661237 Simplifying x + -2.25974026 = -0.7661237 Reorder the terms: -2.25974026 + x = -0.7661237 Solving -2.25974026 + x = -0.7661237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25974026' to each side of the equation. -2.25974026 + 2.25974026 + x = -0.7661237 + 2.25974026 Combine like terms: -2.25974026 + 2.25974026 = 0.00000000 0.00000000 + x = -0.7661237 + 2.25974026 x = -0.7661237 + 2.25974026 Combine like terms: -0.7661237 + 2.25974026 = 1.49361656 x = 1.49361656 Simplifying x = 1.49361656Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.02586396, 1.49361656}
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