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Simplifying 16x2 + -38x + -21 = 0 Reorder the terms: -21 + -38x + 16x2 = 0 Solving -21 + -38x + 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'. -1.3125 + -2.375x + x2 = 0 Move the constant term to the right: Add '1.3125' to each side of the equation. -1.3125 + -2.375x + 1.3125 + x2 = 0 + 1.3125 Reorder the terms: -1.3125 + 1.3125 + -2.375x + x2 = 0 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + -2.375x + x2 = 0 + 1.3125 -2.375x + x2 = 0 + 1.3125 Combine like terms: 0 + 1.3125 = 1.3125 -2.375x + x2 = 1.3125 The x term is -2.375x. Take half its coefficient (-1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. -2.375x + 1.41015625 + x2 = 1.3125 + 1.41015625 Reorder the terms: 1.41015625 + -2.375x + x2 = 1.3125 + 1.41015625 Combine like terms: 1.3125 + 1.41015625 = 2.72265625 1.41015625 + -2.375x + x2 = 2.72265625 Factor a perfect square on the left side: (x + -1.1875)(x + -1.1875) = 2.72265625 Calculate the square root of the right side: 1.650047348 Break this problem into two subproblems by setting (x + -1.1875) equal to 1.650047348 and -1.650047348.Subproblem 1
x + -1.1875 = 1.650047348 Simplifying x + -1.1875 = 1.650047348 Reorder the terms: -1.1875 + x = 1.650047348 Solving -1.1875 + x = 1.650047348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + x = 1.650047348 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = 1.650047348 + 1.1875 x = 1.650047348 + 1.1875 Combine like terms: 1.650047348 + 1.1875 = 2.837547348 x = 2.837547348 Simplifying x = 2.837547348Subproblem 2
x + -1.1875 = -1.650047348 Simplifying x + -1.1875 = -1.650047348 Reorder the terms: -1.1875 + x = -1.650047348 Solving -1.1875 + x = -1.650047348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + x = -1.650047348 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = -1.650047348 + 1.1875 x = -1.650047348 + 1.1875 Combine like terms: -1.650047348 + 1.1875 = -0.462547348 x = -0.462547348 Simplifying x = -0.462547348Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.837547348, -0.462547348}
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