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Simplifying 7.85x2 + 3.06x = 5.05 Reorder the terms: 3.06x + 7.85x2 = 5.05 Solving 3.06x + 7.85x2 = 5.05 Solving for variable 'x'. Reorder the terms: -5.05 + 3.06x + 7.85x2 = 5.05 + -5.05 Combine like terms: 5.05 + -5.05 = 0.00 -5.05 + 3.06x + 7.85x2 = 0.00 Begin completing the square. Divide all terms by 7.85 the coefficient of the squared term: Divide each side by '7.85'. -0.6433121019 + 0.3898089172x + x2 = 0 Move the constant term to the right: Add '0.6433121019' to each side of the equation. -0.6433121019 + 0.3898089172x + 0.6433121019 + x2 = 0 + 0.6433121019 Reorder the terms: -0.6433121019 + 0.6433121019 + 0.3898089172x + x2 = 0 + 0.6433121019 Combine like terms: -0.6433121019 + 0.6433121019 = 0.0000000000 0.0000000000 + 0.3898089172x + x2 = 0 + 0.6433121019 0.3898089172x + x2 = 0 + 0.6433121019 Combine like terms: 0 + 0.6433121019 = 0.6433121019 0.3898089172x + x2 = 0.6433121019 The x term is 0.3898089172x. Take half its coefficient (0.1949044586). Square it (0.03798774798) and add it to both sides. Add '0.03798774798' to each side of the equation. 0.3898089172x + 0.03798774798 + x2 = 0.6433121019 + 0.03798774798 Reorder the terms: 0.03798774798 + 0.3898089172x + x2 = 0.6433121019 + 0.03798774798 Combine like terms: 0.6433121019 + 0.03798774798 = 0.68129984988 0.03798774798 + 0.3898089172x + x2 = 0.68129984988 Factor a perfect square on the left side: (x + 0.1949044586)(x + 0.1949044586) = 0.68129984988 Calculate the square root of the right side: 0.825408899 Break this problem into two subproblems by setting (x + 0.1949044586) equal to 0.825408899 and -0.825408899.Subproblem 1
x + 0.1949044586 = 0.825408899 Simplifying x + 0.1949044586 = 0.825408899 Reorder the terms: 0.1949044586 + x = 0.825408899 Solving 0.1949044586 + x = 0.825408899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1949044586' to each side of the equation. 0.1949044586 + -0.1949044586 + x = 0.825408899 + -0.1949044586 Combine like terms: 0.1949044586 + -0.1949044586 = 0.0000000000 0.0000000000 + x = 0.825408899 + -0.1949044586 x = 0.825408899 + -0.1949044586 Combine like terms: 0.825408899 + -0.1949044586 = 0.6305044404 x = 0.6305044404 Simplifying x = 0.6305044404Subproblem 2
x + 0.1949044586 = -0.825408899 Simplifying x + 0.1949044586 = -0.825408899 Reorder the terms: 0.1949044586 + x = -0.825408899 Solving 0.1949044586 + x = -0.825408899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1949044586' to each side of the equation. 0.1949044586 + -0.1949044586 + x = -0.825408899 + -0.1949044586 Combine like terms: 0.1949044586 + -0.1949044586 = 0.0000000000 0.0000000000 + x = -0.825408899 + -0.1949044586 x = -0.825408899 + -0.1949044586 Combine like terms: -0.825408899 + -0.1949044586 = -1.0203133576 x = -1.0203133576 Simplifying x = -1.0203133576Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6305044404, -1.0203133576}
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