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Simplifying 1200 = 4x2 + 55x + 1020 Reorder the terms: 1200 = 1020 + 55x + 4x2 Solving 1200 = 1020 + 55x + 4x2 Solving for variable 'x'. Combine like terms: 1200 + -1020 = 180 180 + -55x + -4x2 = 1020 + 55x + 4x2 + -1020 + -55x + -4x2 Reorder the terms: 180 + -55x + -4x2 = 1020 + -1020 + 55x + -55x + 4x2 + -4x2 Combine like terms: 1020 + -1020 = 0 180 + -55x + -4x2 = 0 + 55x + -55x + 4x2 + -4x2 180 + -55x + -4x2 = 55x + -55x + 4x2 + -4x2 Combine like terms: 55x + -55x = 0 180 + -55x + -4x2 = 0 + 4x2 + -4x2 180 + -55x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 180 + -55x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -45 + 13.75x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 13.75x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 13.75x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 13.75x + x2 = 0 + 45 13.75x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 13.75x + x2 = 45 The x term is 13.75x. Take half its coefficient (6.875). Square it (47.265625) and add it to both sides. Add '47.265625' to each side of the equation. 13.75x + 47.265625 + x2 = 45 + 47.265625 Reorder the terms: 47.265625 + 13.75x + x2 = 45 + 47.265625 Combine like terms: 45 + 47.265625 = 92.265625 47.265625 + 13.75x + x2 = 92.265625 Factor a perfect square on the left side: (x + 6.875)(x + 6.875) = 92.265625 Calculate the square root of the right side: 9.605499727 Break this problem into two subproblems by setting (x + 6.875) equal to 9.605499727 and -9.605499727.Subproblem 1
x + 6.875 = 9.605499727 Simplifying x + 6.875 = 9.605499727 Reorder the terms: 6.875 + x = 9.605499727 Solving 6.875 + x = 9.605499727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.875' to each side of the equation. 6.875 + -6.875 + x = 9.605499727 + -6.875 Combine like terms: 6.875 + -6.875 = 0.000 0.000 + x = 9.605499727 + -6.875 x = 9.605499727 + -6.875 Combine like terms: 9.605499727 + -6.875 = 2.730499727 x = 2.730499727 Simplifying x = 2.730499727Subproblem 2
x + 6.875 = -9.605499727 Simplifying x + 6.875 = -9.605499727 Reorder the terms: 6.875 + x = -9.605499727 Solving 6.875 + x = -9.605499727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.875' to each side of the equation. 6.875 + -6.875 + x = -9.605499727 + -6.875 Combine like terms: 6.875 + -6.875 = 0.000 0.000 + x = -9.605499727 + -6.875 x = -9.605499727 + -6.875 Combine like terms: -9.605499727 + -6.875 = -16.480499727 x = -16.480499727 Simplifying x = -16.480499727Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.730499727, -16.480499727}
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