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Simplifying 4x2 + 57.92x + -44.41 = 0 Reorder the terms: -44.41 + 57.92x + 4x2 = 0 Solving -44.41 + 57.92x + 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'. -11.1025 + 14.48x + x2 = 0 Move the constant term to the right: Add '11.1025' to each side of the equation. -11.1025 + 14.48x + 11.1025 + x2 = 0 + 11.1025 Reorder the terms: -11.1025 + 11.1025 + 14.48x + x2 = 0 + 11.1025 Combine like terms: -11.1025 + 11.1025 = 0.0000 0.0000 + 14.48x + x2 = 0 + 11.1025 14.48x + x2 = 0 + 11.1025 Combine like terms: 0 + 11.1025 = 11.1025 14.48x + x2 = 11.1025 The x term is 14.48x. Take half its coefficient (7.24). Square it (52.4176) and add it to both sides. Add '52.4176' to each side of the equation. 14.48x + 52.4176 + x2 = 11.1025 + 52.4176 Reorder the terms: 52.4176 + 14.48x + x2 = 11.1025 + 52.4176 Combine like terms: 11.1025 + 52.4176 = 63.5201 52.4176 + 14.48x + x2 = 63.5201 Factor a perfect square on the left side: (x + 7.24)(x + 7.24) = 63.5201 Calculate the square root of the right side: 7.969949812 Break this problem into two subproblems by setting (x + 7.24) equal to 7.969949812 and -7.969949812.Subproblem 1
x + 7.24 = 7.969949812 Simplifying x + 7.24 = 7.969949812 Reorder the terms: 7.24 + x = 7.969949812 Solving 7.24 + x = 7.969949812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.24' to each side of the equation. 7.24 + -7.24 + x = 7.969949812 + -7.24 Combine like terms: 7.24 + -7.24 = 0.00 0.00 + x = 7.969949812 + -7.24 x = 7.969949812 + -7.24 Combine like terms: 7.969949812 + -7.24 = 0.729949812 x = 0.729949812 Simplifying x = 0.729949812Subproblem 2
x + 7.24 = -7.969949812 Simplifying x + 7.24 = -7.969949812 Reorder the terms: 7.24 + x = -7.969949812 Solving 7.24 + x = -7.969949812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.24' to each side of the equation. 7.24 + -7.24 + x = -7.969949812 + -7.24 Combine like terms: 7.24 + -7.24 = 0.00 0.00 + x = -7.969949812 + -7.24 x = -7.969949812 + -7.24 Combine like terms: -7.969949812 + -7.24 = -15.209949812 x = -15.209949812 Simplifying x = -15.209949812Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.729949812, -15.209949812}
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