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Simplifying 16x2 + -22x = 37 Reorder the terms: -22x + 16x2 = 37 Solving -22x + 16x2 = 37 Solving for variable 'x'. Reorder the terms: -37 + -22x + 16x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + -22x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.3125 + -1.375x + x2 = 0 Move the constant term to the right: Add '2.3125' to each side of the equation. -2.3125 + -1.375x + 2.3125 + x2 = 0 + 2.3125 Reorder the terms: -2.3125 + 2.3125 + -1.375x + x2 = 0 + 2.3125 Combine like terms: -2.3125 + 2.3125 = 0.0000 0.0000 + -1.375x + x2 = 0 + 2.3125 -1.375x + x2 = 0 + 2.3125 Combine like terms: 0 + 2.3125 = 2.3125 -1.375x + x2 = 2.3125 The x term is -1.375x. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375x + 0.47265625 + x2 = 2.3125 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = 2.3125 + 0.47265625 Combine like terms: 2.3125 + 0.47265625 = 2.78515625 0.47265625 + -1.375x + x2 = 2.78515625 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = 2.78515625 Calculate the square root of the right side: 1.66887874 Break this problem into two subproblems by setting (x + -0.6875) equal to 1.66887874 and -1.66887874.Subproblem 1
x + -0.6875 = 1.66887874 Simplifying x + -0.6875 = 1.66887874 Reorder the terms: -0.6875 + x = 1.66887874 Solving -0.6875 + x = 1.66887874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = 1.66887874 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 1.66887874 + 0.6875 x = 1.66887874 + 0.6875 Combine like terms: 1.66887874 + 0.6875 = 2.35637874 x = 2.35637874 Simplifying x = 2.35637874Subproblem 2
x + -0.6875 = -1.66887874 Simplifying x + -0.6875 = -1.66887874 Reorder the terms: -0.6875 + x = -1.66887874 Solving -0.6875 + x = -1.66887874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = -1.66887874 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -1.66887874 + 0.6875 x = -1.66887874 + 0.6875 Combine like terms: -1.66887874 + 0.6875 = -0.98137874 x = -0.98137874 Simplifying x = -0.98137874Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.35637874, -0.98137874}
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