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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 = 1.6957063855 x = 1.6957063855 Simplifying x = 1.6957063855Subproblem 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 = -0.6290397185 x = -0.6290397185 Simplifying x = -0.6290397185Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6957063855, -0.6290397185}
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