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Simplifying 16x2 + -89x + -9 = 0 Reorder the terms: -9 + -89x + 16x2 = 0 Solving -9 + -89x + 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'. -0.5625 + -5.5625x + x2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -5.5625x + 0.5625 + x2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -5.5625x + x2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -5.5625x + x2 = 0 + 0.5625 -5.5625x + x2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -5.5625x + x2 = 0.5625 The x term is -5.5625x. Take half its coefficient (-2.78125). Square it (7.735351563) and add it to both sides. Add '7.735351563' to each side of the equation. -5.5625x + 7.735351563 + x2 = 0.5625 + 7.735351563 Reorder the terms: 7.735351563 + -5.5625x + x2 = 0.5625 + 7.735351563 Combine like terms: 0.5625 + 7.735351563 = 8.297851563 7.735351563 + -5.5625x + x2 = 8.297851563 Factor a perfect square on the left side: (x + -2.78125)(x + -2.78125) = 8.297851563 Calculate the square root of the right side: 2.880599167 Break this problem into two subproblems by setting (x + -2.78125) equal to 2.880599167 and -2.880599167.Subproblem 1
x + -2.78125 = 2.880599167 Simplifying x + -2.78125 = 2.880599167 Reorder the terms: -2.78125 + x = 2.880599167 Solving -2.78125 + x = 2.880599167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.78125' to each side of the equation. -2.78125 + 2.78125 + x = 2.880599167 + 2.78125 Combine like terms: -2.78125 + 2.78125 = 0.00000 0.00000 + x = 2.880599167 + 2.78125 x = 2.880599167 + 2.78125 Combine like terms: 2.880599167 + 2.78125 = 5.661849167 x = 5.661849167 Simplifying x = 5.661849167Subproblem 2
x + -2.78125 = -2.880599167 Simplifying x + -2.78125 = -2.880599167 Reorder the terms: -2.78125 + x = -2.880599167 Solving -2.78125 + x = -2.880599167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.78125' to each side of the equation. -2.78125 + 2.78125 + x = -2.880599167 + 2.78125 Combine like terms: -2.78125 + 2.78125 = 0.00000 0.00000 + x = -2.880599167 + 2.78125 x = -2.880599167 + 2.78125 Combine like terms: -2.880599167 + 2.78125 = -0.099349167 x = -0.099349167 Simplifying x = -0.099349167Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.661849167, -0.099349167}
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