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Simplifying 16x2 + -64x + 19 = 0 Reorder the terms: 19 + -64x + 16x2 = 0 Solving 19 + -64x + 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'. 1.1875 + -4x + x2 = 0 Move the constant term to the right: Add '-1.1875' to each side of the equation. 1.1875 + -4x + -1.1875 + x2 = 0 + -1.1875 Reorder the terms: 1.1875 + -1.1875 + -4x + x2 = 0 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + -4x + x2 = 0 + -1.1875 -4x + x2 = 0 + -1.1875 Combine like terms: 0 + -1.1875 = -1.1875 -4x + x2 = -1.1875 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -1.1875 + 4 Reorder the terms: 4 + -4x + x2 = -1.1875 + 4 Combine like terms: -1.1875 + 4 = 2.8125 4 + -4x + x2 = 2.8125 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (x + -2) equal to 1.677050983 and -1.677050983.Subproblem 1
x + -2 = 1.677050983 Simplifying x + -2 = 1.677050983 Reorder the terms: -2 + x = 1.677050983 Solving -2 + x = 1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.677050983 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.677050983 + 2 x = 1.677050983 + 2 Combine like terms: 1.677050983 + 2 = 3.677050983 x = 3.677050983 Simplifying x = 3.677050983Subproblem 2
x + -2 = -1.677050983 Simplifying x + -2 = -1.677050983 Reorder the terms: -2 + x = -1.677050983 Solving -2 + x = -1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.677050983 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.677050983 + 2 x = -1.677050983 + 2 Combine like terms: -1.677050983 + 2 = 0.322949017 x = 0.322949017 Simplifying x = 0.322949017Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.677050983, 0.322949017}
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