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Simplifying -16x2 + 9.7x + 24.61 = 0 Reorder the terms: 24.61 + 9.7x + -16x2 = 0 Solving 24.61 + 9.7x + -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'. -1.538125 + -0.60625x + x2 = 0 Move the constant term to the right: Add '1.538125' to each side of the equation. -1.538125 + -0.60625x + 1.538125 + x2 = 0 + 1.538125 Reorder the terms: -1.538125 + 1.538125 + -0.60625x + x2 = 0 + 1.538125 Combine like terms: -1.538125 + 1.538125 = 0.000000 0.000000 + -0.60625x + x2 = 0 + 1.538125 -0.60625x + x2 = 0 + 1.538125 Combine like terms: 0 + 1.538125 = 1.538125 -0.60625x + x2 = 1.538125 The x term is -0.60625x. Take half its coefficient (-0.303125). Square it (0.09188476563) and add it to both sides. Add '0.09188476563' to each side of the equation. -0.60625x + 0.09188476563 + x2 = 1.538125 + 0.09188476563 Reorder the terms: 0.09188476563 + -0.60625x + x2 = 1.538125 + 0.09188476563 Combine like terms: 1.538125 + 0.09188476563 = 1.63000976563 0.09188476563 + -0.60625x + x2 = 1.63000976563 Factor a perfect square on the left side: (x + -0.303125)(x + -0.303125) = 1.63000976563 Calculate the square root of the right side: 1.276718358 Break this problem into two subproblems by setting (x + -0.303125) equal to 1.276718358 and -1.276718358.Subproblem 1
x + -0.303125 = 1.276718358 Simplifying x + -0.303125 = 1.276718358 Reorder the terms: -0.303125 + x = 1.276718358 Solving -0.303125 + x = 1.276718358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.303125' to each side of the equation. -0.303125 + 0.303125 + x = 1.276718358 + 0.303125 Combine like terms: -0.303125 + 0.303125 = 0.000000 0.000000 + x = 1.276718358 + 0.303125 x = 1.276718358 + 0.303125 Combine like terms: 1.276718358 + 0.303125 = 1.579843358 x = 1.579843358 Simplifying x = 1.579843358Subproblem 2
x + -0.303125 = -1.276718358 Simplifying x + -0.303125 = -1.276718358 Reorder the terms: -0.303125 + x = -1.276718358 Solving -0.303125 + x = -1.276718358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.303125' to each side of the equation. -0.303125 + 0.303125 + x = -1.276718358 + 0.303125 Combine like terms: -0.303125 + 0.303125 = 0.000000 0.000000 + x = -1.276718358 + 0.303125 x = -1.276718358 + 0.303125 Combine like terms: -1.276718358 + 0.303125 = -0.973593358 x = -0.973593358 Simplifying x = -0.973593358Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.579843358, -0.973593358}
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