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Simplifying 16x2 + -72x + -169 = 0 Reorder the terms: -169 + -72x + 16x2 = 0 Solving -169 + -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'. -10.5625 + -4.5x + x2 = 0 Move the constant term to the right: Add '10.5625' to each side of the equation. -10.5625 + -4.5x + 10.5625 + x2 = 0 + 10.5625 Reorder the terms: -10.5625 + 10.5625 + -4.5x + x2 = 0 + 10.5625 Combine like terms: -10.5625 + 10.5625 = 0.0000 0.0000 + -4.5x + x2 = 0 + 10.5625 -4.5x + x2 = 0 + 10.5625 Combine like terms: 0 + 10.5625 = 10.5625 -4.5x + x2 = 10.5625 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 = 10.5625 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 10.5625 + 5.0625 Combine like terms: 10.5625 + 5.0625 = 15.625 5.0625 + -4.5x + x2 = 15.625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 15.625 Calculate the square root of the right side: 3.952847075 Break this problem into two subproblems by setting (x + -2.25) equal to 3.952847075 and -3.952847075.Subproblem 1
x + -2.25 = 3.952847075 Simplifying x + -2.25 = 3.952847075 Reorder the terms: -2.25 + x = 3.952847075 Solving -2.25 + x = 3.952847075 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 = 3.952847075 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 3.952847075 + 2.25 x = 3.952847075 + 2.25 Combine like terms: 3.952847075 + 2.25 = 6.202847075 x = 6.202847075 Simplifying x = 6.202847075Subproblem 2
x + -2.25 = -3.952847075 Simplifying x + -2.25 = -3.952847075 Reorder the terms: -2.25 + x = -3.952847075 Solving -2.25 + x = -3.952847075 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 = -3.952847075 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -3.952847075 + 2.25 x = -3.952847075 + 2.25 Combine like terms: -3.952847075 + 2.25 = -1.702847075 x = -1.702847075 Simplifying x = -1.702847075Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.202847075, -1.702847075}
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