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Simplifying 15x2 + 16x + -16 = 0 Reorder the terms: -16 + 16x + 15x2 = 0 Solving -16 + 16x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.066666667 + 1.066666667x + x2 = 0 Move the constant term to the right: Add '1.066666667' to each side of the equation. -1.066666667 + 1.066666667x + 1.066666667 + x2 = 0 + 1.066666667 Reorder the terms: -1.066666667 + 1.066666667 + 1.066666667x + x2 = 0 + 1.066666667 Combine like terms: -1.066666667 + 1.066666667 = 0.000000000 0.000000000 + 1.066666667x + x2 = 0 + 1.066666667 1.066666667x + x2 = 0 + 1.066666667 Combine like terms: 0 + 1.066666667 = 1.066666667 1.066666667x + x2 = 1.066666667 The x term is 1.066666667x. Take half its coefficient (0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. 1.066666667x + 0.2844444446 + x2 = 1.066666667 + 0.2844444446 Reorder the terms: 0.2844444446 + 1.066666667x + x2 = 1.066666667 + 0.2844444446 Combine like terms: 1.066666667 + 0.2844444446 = 1.3511111116 0.2844444446 + 1.066666667x + x2 = 1.3511111116 Factor a perfect square on the left side: (x + 0.5333333335)(x + 0.5333333335) = 1.3511111116 Calculate the square root of the right side: 1.162373052 Break this problem into two subproblems by setting (x + 0.5333333335) equal to 1.162373052 and -1.162373052.Subproblem 1
x + 0.5333333335 = 1.162373052 Simplifying x + 0.5333333335 = 1.162373052 Reorder the terms: 0.5333333335 + x = 1.162373052 Solving 0.5333333335 + x = 1.162373052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5333333335' to each side of the equation. 0.5333333335 + -0.5333333335 + x = 1.162373052 + -0.5333333335 Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000 0.0000000000 + x = 1.162373052 + -0.5333333335 x = 1.162373052 + -0.5333333335 Combine like terms: 1.162373052 + -0.5333333335 = 0.6290397185 x = 0.6290397185 Simplifying x = 0.6290397185Subproblem 2
x + 0.5333333335 = -1.162373052 Simplifying x + 0.5333333335 = -1.162373052 Reorder the terms: 0.5333333335 + x = -1.162373052 Solving 0.5333333335 + x = -1.162373052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5333333335' to each side of the equation. 0.5333333335 + -0.5333333335 + x = -1.162373052 + -0.5333333335 Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000 0.0000000000 + x = -1.162373052 + -0.5333333335 x = -1.162373052 + -0.5333333335 Combine like terms: -1.162373052 + -0.5333333335 = -1.6957063855 x = -1.6957063855 Simplifying x = -1.6957063855Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6290397185, -1.6957063855}
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