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Simplifying 16x2 + -72x + -49 = 0 Reorder the terms: -49 + -72x + 16x2 = 0 Solving -49 + -72x + 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'. -3.0625 + -4.5x + x2 = 0 Move the constant term to the right: Add '3.0625' to each side of the equation. -3.0625 + -4.5x + 3.0625 + x2 = 0 + 3.0625 Reorder the terms: -3.0625 + 3.0625 + -4.5x + x2 = 0 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + -4.5x + x2 = 0 + 3.0625 -4.5x + x2 = 0 + 3.0625 Combine like terms: 0 + 3.0625 = 3.0625 -4.5x + x2 = 3.0625 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 3.0625 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 3.0625 + 5.0625 Combine like terms: 3.0625 + 5.0625 = 8.125 5.0625 + -4.5x + x2 = 8.125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 8.125 Calculate the square root of the right side: 2.850438563 Break this problem into two subproblems by setting (x + -2.25) equal to 2.850438563 and -2.850438563.Subproblem 1
x + -2.25 = 2.850438563 Simplifying x + -2.25 = 2.850438563 Reorder the terms: -2.25 + x = 2.850438563 Solving -2.25 + x = 2.850438563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.850438563 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.850438563 + 2.25 x = 2.850438563 + 2.25 Combine like terms: 2.850438563 + 2.25 = 5.100438563 x = 5.100438563 Simplifying x = 5.100438563Subproblem 2
x + -2.25 = -2.850438563 Simplifying x + -2.25 = -2.850438563 Reorder the terms: -2.25 + x = -2.850438563 Solving -2.25 + x = -2.850438563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.850438563 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.850438563 + 2.25 x = -2.850438563 + 2.25 Combine like terms: -2.850438563 + 2.25 = -0.600438563 x = -0.600438563 Simplifying x = -0.600438563Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.100438563, -0.600438563}
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