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Simplifying 4x2 + 49x + 30 = 0 Reorder the terms: 30 + 49x + 4x2 = 0 Solving 30 + 49x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.5 + 12.25x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 12.25x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 12.25x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 12.25x + x2 = 0 + -7.5 12.25x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 12.25x + x2 = -7.5 The x term is 12.25x. Take half its coefficient (6.125). Square it (37.515625) and add it to both sides. Add '37.515625' to each side of the equation. 12.25x + 37.515625 + x2 = -7.5 + 37.515625 Reorder the terms: 37.515625 + 12.25x + x2 = -7.5 + 37.515625 Combine like terms: -7.5 + 37.515625 = 30.015625 37.515625 + 12.25x + x2 = 30.015625 Factor a perfect square on the left side: (x + 6.125)(x + 6.125) = 30.015625 Calculate the square root of the right side: 5.47865175 Break this problem into two subproblems by setting (x + 6.125) equal to 5.47865175 and -5.47865175.Subproblem 1
x + 6.125 = 5.47865175 Simplifying x + 6.125 = 5.47865175 Reorder the terms: 6.125 + x = 5.47865175 Solving 6.125 + x = 5.47865175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.125' to each side of the equation. 6.125 + -6.125 + x = 5.47865175 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + x = 5.47865175 + -6.125 x = 5.47865175 + -6.125 Combine like terms: 5.47865175 + -6.125 = -0.64634825 x = -0.64634825 Simplifying x = -0.64634825Subproblem 2
x + 6.125 = -5.47865175 Simplifying x + 6.125 = -5.47865175 Reorder the terms: 6.125 + x = -5.47865175 Solving 6.125 + x = -5.47865175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.125' to each side of the equation. 6.125 + -6.125 + x = -5.47865175 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + x = -5.47865175 + -6.125 x = -5.47865175 + -6.125 Combine like terms: -5.47865175 + -6.125 = -11.60365175 x = -11.60365175 Simplifying x = -11.60365175Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.64634825, -11.60365175}
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