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Simplifying 16x2 + -120x + -225 = 0 Reorder the terms: -225 + -120x + 16x2 = 0 Solving -225 + -120x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -14.0625 + -7.5x + x2 = 0 Move the constant term to the right: Add '14.0625' to each side of the equation. -14.0625 + -7.5x + 14.0625 + x2 = 0 + 14.0625 Reorder the terms: -14.0625 + 14.0625 + -7.5x + x2 = 0 + 14.0625 Combine like terms: -14.0625 + 14.0625 = 0.0000 0.0000 + -7.5x + x2 = 0 + 14.0625 -7.5x + x2 = 0 + 14.0625 Combine like terms: 0 + 14.0625 = 14.0625 -7.5x + x2 = 14.0625 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 14.0625 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 14.0625 + 14.0625 Combine like terms: 14.0625 + 14.0625 = 28.125 14.0625 + -7.5x + x2 = 28.125 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 28.125 Calculate the square root of the right side: 5.303300859 Break this problem into two subproblems by setting (x + -3.75) equal to 5.303300859 and -5.303300859.Subproblem 1
x + -3.75 = 5.303300859 Simplifying x + -3.75 = 5.303300859 Reorder the terms: -3.75 + x = 5.303300859 Solving -3.75 + x = 5.303300859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 5.303300859 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 5.303300859 + 3.75 x = 5.303300859 + 3.75 Combine like terms: 5.303300859 + 3.75 = 9.053300859 x = 9.053300859 Simplifying x = 9.053300859Subproblem 2
x + -3.75 = -5.303300859 Simplifying x + -3.75 = -5.303300859 Reorder the terms: -3.75 + x = -5.303300859 Solving -3.75 + x = -5.303300859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -5.303300859 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -5.303300859 + 3.75 x = -5.303300859 + 3.75 Combine like terms: -5.303300859 + 3.75 = -1.553300859 x = -1.553300859 Simplifying x = -1.553300859Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.053300859, -1.553300859}
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