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Simplifying -0.04x2 + 5.8x + 4.9 = 0 Reorder the terms: 4.9 + 5.8x + -0.04x2 = 0 Solving 4.9 + 5.8x + -0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -122.5 + -145x + x2 = 0 Move the constant term to the right: Add '122.5' to each side of the equation. -122.5 + -145x + 122.5 + x2 = 0 + 122.5 Reorder the terms: -122.5 + 122.5 + -145x + x2 = 0 + 122.5 Combine like terms: -122.5 + 122.5 = 0.0 0.0 + -145x + x2 = 0 + 122.5 -145x + x2 = 0 + 122.5 Combine like terms: 0 + 122.5 = 122.5 -145x + x2 = 122.5 The x term is -145x. Take half its coefficient (-72.5). Square it (5256.25) and add it to both sides. Add '5256.25' to each side of the equation. -145x + 5256.25 + x2 = 122.5 + 5256.25 Reorder the terms: 5256.25 + -145x + x2 = 122.5 + 5256.25 Combine like terms: 122.5 + 5256.25 = 5378.75 5256.25 + -145x + x2 = 5378.75 Factor a perfect square on the left side: (x + -72.5)(x + -72.5) = 5378.75 Calculate the square root of the right side: 73.339961822 Break this problem into two subproblems by setting (x + -72.5) equal to 73.339961822 and -73.339961822.Subproblem 1
x + -72.5 = 73.339961822 Simplifying x + -72.5 = 73.339961822 Reorder the terms: -72.5 + x = 73.339961822 Solving -72.5 + x = 73.339961822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72.5' to each side of the equation. -72.5 + 72.5 + x = 73.339961822 + 72.5 Combine like terms: -72.5 + 72.5 = 0.0 0.0 + x = 73.339961822 + 72.5 x = 73.339961822 + 72.5 Combine like terms: 73.339961822 + 72.5 = 145.839961822 x = 145.839961822 Simplifying x = 145.839961822Subproblem 2
x + -72.5 = -73.339961822 Simplifying x + -72.5 = -73.339961822 Reorder the terms: -72.5 + x = -73.339961822 Solving -72.5 + x = -73.339961822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72.5' to each side of the equation. -72.5 + 72.5 + x = -73.339961822 + 72.5 Combine like terms: -72.5 + 72.5 = 0.0 0.0 + x = -73.339961822 + 72.5 x = -73.339961822 + 72.5 Combine like terms: -73.339961822 + 72.5 = -0.839961822 x = -0.839961822 Simplifying x = -0.839961822Solution
The solution to the problem is based on the solutions from the subproblems. x = {145.839961822, -0.839961822}
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