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Simplifying -16x2 + 9x + 650 = 0 Reorder the terms: 650 + 9x + -16x2 = 0 Solving 650 + 9x + -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'. -40.625 + -0.5625x + x2 = 0 Move the constant term to the right: Add '40.625' to each side of the equation. -40.625 + -0.5625x + 40.625 + x2 = 0 + 40.625 Reorder the terms: -40.625 + 40.625 + -0.5625x + x2 = 0 + 40.625 Combine like terms: -40.625 + 40.625 = 0.000 0.000 + -0.5625x + x2 = 0 + 40.625 -0.5625x + x2 = 0 + 40.625 Combine like terms: 0 + 40.625 = 40.625 -0.5625x + x2 = 40.625 The x term is -0.5625x. Take half its coefficient (-0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. -0.5625x + 0.0791015625 + x2 = 40.625 + 0.0791015625 Reorder the terms: 0.0791015625 + -0.5625x + x2 = 40.625 + 0.0791015625 Combine like terms: 40.625 + 0.0791015625 = 40.7041015625 0.0791015625 + -0.5625x + x2 = 40.7041015625 Factor a perfect square on the left side: (x + -0.28125)(x + -0.28125) = 40.7041015625 Calculate the square root of the right side: 6.379976611 Break this problem into two subproblems by setting (x + -0.28125) equal to 6.379976611 and -6.379976611.Subproblem 1
x + -0.28125 = 6.379976611 Simplifying x + -0.28125 = 6.379976611 Reorder the terms: -0.28125 + x = 6.379976611 Solving -0.28125 + x = 6.379976611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = 6.379976611 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = 6.379976611 + 0.28125 x = 6.379976611 + 0.28125 Combine like terms: 6.379976611 + 0.28125 = 6.661226611 x = 6.661226611 Simplifying x = 6.661226611Subproblem 2
x + -0.28125 = -6.379976611 Simplifying x + -0.28125 = -6.379976611 Reorder the terms: -0.28125 + x = -6.379976611 Solving -0.28125 + x = -6.379976611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = -6.379976611 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = -6.379976611 + 0.28125 x = -6.379976611 + 0.28125 Combine like terms: -6.379976611 + 0.28125 = -6.098726611 x = -6.098726611 Simplifying x = -6.098726611Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.661226611, -6.098726611}
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