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Simplifying 30x2 + x + -56 = 0 Reorder the terms: -56 + x + 30x2 = 0 Solving -56 + x + 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'. -1.866666667 + 0.03333333333x + x2 = 0 Move the constant term to the right: Add '1.866666667' to each side of the equation. -1.866666667 + 0.03333333333x + 1.866666667 + x2 = 0 + 1.866666667 Reorder the terms: -1.866666667 + 1.866666667 + 0.03333333333x + x2 = 0 + 1.866666667 Combine like terms: -1.866666667 + 1.866666667 = 0.000000000 0.000000000 + 0.03333333333x + x2 = 0 + 1.866666667 0.03333333333x + x2 = 0 + 1.866666667 Combine like terms: 0 + 1.866666667 = 1.866666667 0.03333333333x + x2 = 1.866666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.03333333333x + 0.25 + x2 = 1.866666667 + 0.25 Reorder the terms: 0.25 + 0.03333333333x + x2 = 1.866666667 + 0.25 Combine like terms: 1.866666667 + 0.25 = 2.116666667 0.25 + 0.03333333333x + x2 = 2.116666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.116666667 Calculate the square root of the right side: 1.454876856 Break this problem into two subproblems by setting (x + 0.5) equal to 1.454876856 and -1.454876856.Subproblem 1
x + 0.5 = 1.454876856 Simplifying x + 0.5 = 1.454876856 Reorder the terms: 0.5 + x = 1.454876856 Solving 0.5 + x = 1.454876856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.454876856 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.454876856 + -0.5 x = 1.454876856 + -0.5 Combine like terms: 1.454876856 + -0.5 = 0.954876856 x = 0.954876856 Simplifying x = 0.954876856Subproblem 2
x + 0.5 = -1.454876856 Simplifying x + 0.5 = -1.454876856 Reorder the terms: 0.5 + x = -1.454876856 Solving 0.5 + x = -1.454876856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.454876856 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.454876856 + -0.5 x = -1.454876856 + -0.5 Combine like terms: -1.454876856 + -0.5 = -1.954876856 x = -1.954876856 Simplifying x = -1.954876856Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.954876856, -1.954876856}
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