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Simplifying 16x2 + -36x + 3 = 0 Reorder the terms: 3 + -36x + 16x2 = 0 Solving 3 + -36x + 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 + -2.25x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -2.25x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -2.25x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -2.25x + x2 = 0 + -0.1875 -2.25x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -2.25x + x2 = -0.1875 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = -0.1875 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = -0.1875 + 1.265625 Combine like terms: -0.1875 + 1.265625 = 1.078125 1.265625 + -2.25x + x2 = 1.078125 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 1.078125 Calculate the square root of the right side: 1.038327983 Break this problem into two subproblems by setting (x + -1.125) equal to 1.038327983 and -1.038327983.Subproblem 1
x + -1.125 = 1.038327983 Simplifying x + -1.125 = 1.038327983 Reorder the terms: -1.125 + x = 1.038327983 Solving -1.125 + x = 1.038327983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.038327983 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.038327983 + 1.125 x = 1.038327983 + 1.125 Combine like terms: 1.038327983 + 1.125 = 2.163327983 x = 2.163327983 Simplifying x = 2.163327983Subproblem 2
x + -1.125 = -1.038327983 Simplifying x + -1.125 = -1.038327983 Reorder the terms: -1.125 + x = -1.038327983 Solving -1.125 + x = -1.038327983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.038327983 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.038327983 + 1.125 x = -1.038327983 + 1.125 Combine like terms: -1.038327983 + 1.125 = 0.086672017 x = 0.086672017 Simplifying x = 0.086672017Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.163327983, 0.086672017}
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