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Simplifying 16x2 + -49x + 36 = 0 Reorder the terms: 36 + -49x + 16x2 = 0 Solving 36 + -49x + 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'. 2.25 + -3.0625x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -3.0625x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -3.0625x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -3.0625x + x2 = 0 + -2.25 -3.0625x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -3.0625x + x2 = -2.25 The x term is -3.0625x. Take half its coefficient (-1.53125). Square it (2.344726563) and add it to both sides. Add '2.344726563' to each side of the equation. -3.0625x + 2.344726563 + x2 = -2.25 + 2.344726563 Reorder the terms: 2.344726563 + -3.0625x + x2 = -2.25 + 2.344726563 Combine like terms: -2.25 + 2.344726563 = 0.094726563 2.344726563 + -3.0625x + x2 = 0.094726563 Factor a perfect square on the left side: (x + -1.53125)(x + -1.53125) = 0.094726563 Calculate the square root of the right side: 0.307776807 Break this problem into two subproblems by setting (x + -1.53125) equal to 0.307776807 and -0.307776807.Subproblem 1
x + -1.53125 = 0.307776807 Simplifying x + -1.53125 = 0.307776807 Reorder the terms: -1.53125 + x = 0.307776807 Solving -1.53125 + x = 0.307776807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.53125' to each side of the equation. -1.53125 + 1.53125 + x = 0.307776807 + 1.53125 Combine like terms: -1.53125 + 1.53125 = 0.00000 0.00000 + x = 0.307776807 + 1.53125 x = 0.307776807 + 1.53125 Combine like terms: 0.307776807 + 1.53125 = 1.839026807 x = 1.839026807 Simplifying x = 1.839026807Subproblem 2
x + -1.53125 = -0.307776807 Simplifying x + -1.53125 = -0.307776807 Reorder the terms: -1.53125 + x = -0.307776807 Solving -1.53125 + x = -0.307776807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.53125' to each side of the equation. -1.53125 + 1.53125 + x = -0.307776807 + 1.53125 Combine like terms: -1.53125 + 1.53125 = 0.00000 0.00000 + x = -0.307776807 + 1.53125 x = -0.307776807 + 1.53125 Combine like terms: -0.307776807 + 1.53125 = 1.223473193 x = 1.223473193 Simplifying x = 1.223473193Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.839026807, 1.223473193}
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