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Simplifying -0.018x2 + -8x + -510 = 0 Reorder the terms: -510 + -8x + -0.018x2 = 0 Solving -510 + -8x + -0.018x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.018 the coefficient of the squared term: Divide each side by '-0.018'. 28333.33333 + 444.4444444x + x2 = 0 Move the constant term to the right: Add '-28333.33333' to each side of the equation. 28333.33333 + 444.4444444x + -28333.33333 + x2 = 0 + -28333.33333 Reorder the terms: 28333.33333 + -28333.33333 + 444.4444444x + x2 = 0 + -28333.33333 Combine like terms: 28333.33333 + -28333.33333 = 0.00000 0.00000 + 444.4444444x + x2 = 0 + -28333.33333 444.4444444x + x2 = 0 + -28333.33333 Combine like terms: 0 + -28333.33333 = -28333.33333 444.4444444x + x2 = -28333.33333 The x term is 444.4444444x. Take half its coefficient (222.2222222). Square it (49382.71604) and add it to both sides. Add '49382.71604' to each side of the equation. 444.4444444x + 49382.71604 + x2 = -28333.33333 + 49382.71604 Reorder the terms: 49382.71604 + 444.4444444x + x2 = -28333.33333 + 49382.71604 Combine like terms: -28333.33333 + 49382.71604 = 21049.38271 49382.71604 + 444.4444444x + x2 = 21049.38271 Factor a perfect square on the left side: (x + 222.2222222)(x + 222.2222222) = 21049.38271 Calculate the square root of the right side: 145.084053948 Break this problem into two subproblems by setting (x + 222.2222222) equal to 145.084053948 and -145.084053948.Subproblem 1
x + 222.2222222 = 145.084053948 Simplifying x + 222.2222222 = 145.084053948 Reorder the terms: 222.2222222 + x = 145.084053948 Solving 222.2222222 + x = 145.084053948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-222.2222222' to each side of the equation. 222.2222222 + -222.2222222 + x = 145.084053948 + -222.2222222 Combine like terms: 222.2222222 + -222.2222222 = 0.0000000 0.0000000 + x = 145.084053948 + -222.2222222 x = 145.084053948 + -222.2222222 Combine like terms: 145.084053948 + -222.2222222 = -77.138168252 x = -77.138168252 Simplifying x = -77.138168252Subproblem 2
x + 222.2222222 = -145.084053948 Simplifying x + 222.2222222 = -145.084053948 Reorder the terms: 222.2222222 + x = -145.084053948 Solving 222.2222222 + x = -145.084053948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-222.2222222' to each side of the equation. 222.2222222 + -222.2222222 + x = -145.084053948 + -222.2222222 Combine like terms: 222.2222222 + -222.2222222 = 0.0000000 0.0000000 + x = -145.084053948 + -222.2222222 x = -145.084053948 + -222.2222222 Combine like terms: -145.084053948 + -222.2222222 = -367.306276148 x = -367.306276148 Simplifying x = -367.306276148Solution
The solution to the problem is based on the solutions from the subproblems. x = {-77.138168252, -367.306276148}
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