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Simplifying -0.003x2 + 0.578x + -0.763 = 0 Reorder the terms: -0.763 + 0.578x + -0.003x2 = 0 Solving -0.763 + 0.578x + -0.003x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.003 the coefficient of the squared term: Divide each side by '-0.003'. 254.3333333 + -192.6666667x + x2 = 0 Move the constant term to the right: Add '-254.3333333' to each side of the equation. 254.3333333 + -192.6666667x + -254.3333333 + x2 = 0 + -254.3333333 Reorder the terms: 254.3333333 + -254.3333333 + -192.6666667x + x2 = 0 + -254.3333333 Combine like terms: 254.3333333 + -254.3333333 = 0.0000000 0.0000000 + -192.6666667x + x2 = 0 + -254.3333333 -192.6666667x + x2 = 0 + -254.3333333 Combine like terms: 0 + -254.3333333 = -254.3333333 -192.6666667x + x2 = -254.3333333 The x term is -192.6666667x. Take half its coefficient (-96.33333335). Square it (9280.111114) and add it to both sides. Add '9280.111114' to each side of the equation. -192.6666667x + 9280.111114 + x2 = -254.3333333 + 9280.111114 Reorder the terms: 9280.111114 + -192.6666667x + x2 = -254.3333333 + 9280.111114 Combine like terms: -254.3333333 + 9280.111114 = 9025.7777807 9280.111114 + -192.6666667x + x2 = 9025.7777807 Factor a perfect square on the left side: (x + -96.33333335)(x + -96.33333335) = 9025.7777807 Calculate the square root of the right side: 95.004093494 Break this problem into two subproblems by setting (x + -96.33333335) equal to 95.004093494 and -95.004093494.Subproblem 1
x + -96.33333335 = 95.004093494 Simplifying x + -96.33333335 = 95.004093494 Reorder the terms: -96.33333335 + x = 95.004093494 Solving -96.33333335 + x = 95.004093494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '96.33333335' to each side of the equation. -96.33333335 + 96.33333335 + x = 95.004093494 + 96.33333335 Combine like terms: -96.33333335 + 96.33333335 = 0.00000000 0.00000000 + x = 95.004093494 + 96.33333335 x = 95.004093494 + 96.33333335 Combine like terms: 95.004093494 + 96.33333335 = 191.337426844 x = 191.337426844 Simplifying x = 191.337426844Subproblem 2
x + -96.33333335 = -95.004093494 Simplifying x + -96.33333335 = -95.004093494 Reorder the terms: -96.33333335 + x = -95.004093494 Solving -96.33333335 + x = -95.004093494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '96.33333335' to each side of the equation. -96.33333335 + 96.33333335 + x = -95.004093494 + 96.33333335 Combine like terms: -96.33333335 + 96.33333335 = 0.00000000 0.00000000 + x = -95.004093494 + 96.33333335 x = -95.004093494 + 96.33333335 Combine like terms: -95.004093494 + 96.33333335 = 1.329239856 x = 1.329239856 Simplifying x = 1.329239856Solution
The solution to the problem is based on the solutions from the subproblems. x = {191.337426844, 1.329239856}
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