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Simplifying -16x2 + 34.92x + 3 = 0 Reorder the terms: 3 + 34.92x + -16x2 = 0 Solving 3 + 34.92x + -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'. -0.1875 + -2.1825x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -2.1825x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -2.1825x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -2.1825x + x2 = 0 + 0.1875 -2.1825x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -2.1825x + x2 = 0.1875 The x term is -2.1825x. Take half its coefficient (-1.09125). Square it (1.190826563) and add it to both sides. Add '1.190826563' to each side of the equation. -2.1825x + 1.190826563 + x2 = 0.1875 + 1.190826563 Reorder the terms: 1.190826563 + -2.1825x + x2 = 0.1875 + 1.190826563 Combine like terms: 0.1875 + 1.190826563 = 1.378326563 1.190826563 + -2.1825x + x2 = 1.378326563 Factor a perfect square on the left side: (x + -1.09125)(x + -1.09125) = 1.378326563 Calculate the square root of the right side: 1.174021534 Break this problem into two subproblems by setting (x + -1.09125) equal to 1.174021534 and -1.174021534.Subproblem 1
x + -1.09125 = 1.174021534 Simplifying x + -1.09125 = 1.174021534 Reorder the terms: -1.09125 + x = 1.174021534 Solving -1.09125 + x = 1.174021534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09125' to each side of the equation. -1.09125 + 1.09125 + x = 1.174021534 + 1.09125 Combine like terms: -1.09125 + 1.09125 = 0.00000 0.00000 + x = 1.174021534 + 1.09125 x = 1.174021534 + 1.09125 Combine like terms: 1.174021534 + 1.09125 = 2.265271534 x = 2.265271534 Simplifying x = 2.265271534Subproblem 2
x + -1.09125 = -1.174021534 Simplifying x + -1.09125 = -1.174021534 Reorder the terms: -1.09125 + x = -1.174021534 Solving -1.09125 + x = -1.174021534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09125' to each side of the equation. -1.09125 + 1.09125 + x = -1.174021534 + 1.09125 Combine like terms: -1.09125 + 1.09125 = 0.00000 0.00000 + x = -1.174021534 + 1.09125 x = -1.174021534 + 1.09125 Combine like terms: -1.174021534 + 1.09125 = -0.082771534 x = -0.082771534 Simplifying x = -0.082771534Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.265271534, -0.082771534}
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