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Simplifying 30x2 + 84x + 55 = 0 Reorder the terms: 55 + 84x + 30x2 = 0 Solving 55 + 84x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 1.833333333 + 2.8x + x2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + 2.8x + -1.833333333 + x2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + 2.8x + x2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + 2.8x + x2 = 0 + -1.833333333 2.8x + x2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 2.8x + x2 = -1.833333333 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = -1.833333333 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = -1.833333333 + 1.96 Combine like terms: -1.833333333 + 1.96 = 0.126666667 1.96 + 2.8x + x2 = 0.126666667 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 0.126666667 Calculate the square root of the right side: 0.355902609 Break this problem into two subproblems by setting (x + 1.4) equal to 0.355902609 and -0.355902609.Subproblem 1
x + 1.4 = 0.355902609 Simplifying x + 1.4 = 0.355902609 Reorder the terms: 1.4 + x = 0.355902609 Solving 1.4 + x = 0.355902609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 0.355902609 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 0.355902609 + -1.4 x = 0.355902609 + -1.4 Combine like terms: 0.355902609 + -1.4 = -1.044097391 x = -1.044097391 Simplifying x = -1.044097391Subproblem 2
x + 1.4 = -0.355902609 Simplifying x + 1.4 = -0.355902609 Reorder the terms: 1.4 + x = -0.355902609 Solving 1.4 + x = -0.355902609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -0.355902609 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -0.355902609 + -1.4 x = -0.355902609 + -1.4 Combine like terms: -0.355902609 + -1.4 = -1.755902609 x = -1.755902609 Simplifying x = -1.755902609Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.044097391, -1.755902609}
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