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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 = 2.265625 47.265625 + -13.75x + x2 = 2.265625 Factor a perfect square on the left side: (x + -6.875)(x + -6.875) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + -6.875) equal to 1.505199322 and -1.505199322.Subproblem 1
x + -6.875 = 1.505199322 Simplifying x + -6.875 = 1.505199322 Reorder the terms: -6.875 + x = 1.505199322 Solving -6.875 + x = 1.505199322 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 = 1.505199322 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + x = 1.505199322 + 6.875 x = 1.505199322 + 6.875 Combine like terms: 1.505199322 + 6.875 = 8.380199322 x = 8.380199322 Simplifying x = 8.380199322Subproblem 2
x + -6.875 = -1.505199322 Simplifying x + -6.875 = -1.505199322 Reorder the terms: -6.875 + x = -1.505199322 Solving -6.875 + x = -1.505199322 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 = -1.505199322 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + x = -1.505199322 + 6.875 x = -1.505199322 + 6.875 Combine like terms: -1.505199322 + 6.875 = 5.369800678 x = 5.369800678 Simplifying x = 5.369800678Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.380199322, 5.369800678}
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