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Simplifying 96x2 + 3.5x + -0.275 = 0 Reorder the terms: -0.275 + 3.5x + 96x2 = 0 Solving -0.275 + 3.5x + 96x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 96 the coefficient of the squared term: Divide each side by '96'. -0.002864583333 + 0.03645833333x + x2 = 0 Move the constant term to the right: Add '0.002864583333' to each side of the equation. -0.002864583333 + 0.03645833333x + 0.002864583333 + x2 = 0 + 0.002864583333 Reorder the terms: -0.002864583333 + 0.002864583333 + 0.03645833333x + x2 = 0 + 0.002864583333 Combine like terms: -0.002864583333 + 0.002864583333 = 0.000000000000 0.000000000000 + 0.03645833333x + x2 = 0 + 0.002864583333 0.03645833333x + x2 = 0 + 0.002864583333 Combine like terms: 0 + 0.002864583333 = 0.002864583333 0.03645833333x + x2 = 0.002864583333 The x term is 0.03645833333x. Take half its coefficient (0.01822916667). Square it (0.0003323025175) and add it to both sides. Add '0.0003323025175' to each side of the equation. 0.03645833333x + 0.0003323025175 + x2 = 0.002864583333 + 0.0003323025175 Reorder the terms: 0.0003323025175 + 0.03645833333x + x2 = 0.002864583333 + 0.0003323025175 Combine like terms: 0.002864583333 + 0.0003323025175 = 0.0031968858505 0.0003323025175 + 0.03645833333x + x2 = 0.0031968858505 Factor a perfect square on the left side: (x + 0.01822916667)(x + 0.01822916667) = 0.0031968858505 Calculate the square root of the right side: 0.05654101 Break this problem into two subproblems by setting (x + 0.01822916667) equal to 0.05654101 and -0.05654101.Subproblem 1
x + 0.01822916667 = 0.05654101 Simplifying x + 0.01822916667 = 0.05654101 Reorder the terms: 0.01822916667 + x = 0.05654101 Solving 0.01822916667 + x = 0.05654101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01822916667' to each side of the equation. 0.01822916667 + -0.01822916667 + x = 0.05654101 + -0.01822916667 Combine like terms: 0.01822916667 + -0.01822916667 = 0.00000000000 0.00000000000 + x = 0.05654101 + -0.01822916667 x = 0.05654101 + -0.01822916667 Combine like terms: 0.05654101 + -0.01822916667 = 0.03831184333 x = 0.03831184333 Simplifying x = 0.03831184333Subproblem 2
x + 0.01822916667 = -0.05654101 Simplifying x + 0.01822916667 = -0.05654101 Reorder the terms: 0.01822916667 + x = -0.05654101 Solving 0.01822916667 + x = -0.05654101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01822916667' to each side of the equation. 0.01822916667 + -0.01822916667 + x = -0.05654101 + -0.01822916667 Combine like terms: 0.01822916667 + -0.01822916667 = 0.00000000000 0.00000000000 + x = -0.05654101 + -0.01822916667 x = -0.05654101 + -0.01822916667 Combine like terms: -0.05654101 + -0.01822916667 = -0.07477017667 x = -0.07477017667 Simplifying x = -0.07477017667Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.03831184333, -0.07477017667}
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