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Simplifying -16x2 + 64x + 119 = 0 Reorder the terms: 119 + 64x + -16x2 = 0 Solving 119 + 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'. -7.4375 + -4x + x2 = 0 Move the constant term to the right: Add '7.4375' to each side of the equation. -7.4375 + -4x + 7.4375 + x2 = 0 + 7.4375 Reorder the terms: -7.4375 + 7.4375 + -4x + x2 = 0 + 7.4375 Combine like terms: -7.4375 + 7.4375 = 0.0000 0.0000 + -4x + x2 = 0 + 7.4375 -4x + x2 = 0 + 7.4375 Combine like terms: 0 + 7.4375 = 7.4375 -4x + x2 = 7.4375 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 = 7.4375 + 4 Reorder the terms: 4 + -4x + x2 = 7.4375 + 4 Combine like terms: 7.4375 + 4 = 11.4375 4 + -4x + x2 = 11.4375 Factor a perfect square on the left side: (x + -2)(x + -2) = 11.4375 Calculate the square root of the right side: 3.381937315 Break this problem into two subproblems by setting (x + -2) equal to 3.381937315 and -3.381937315.Subproblem 1
x + -2 = 3.381937315 Simplifying x + -2 = 3.381937315 Reorder the terms: -2 + x = 3.381937315 Solving -2 + x = 3.381937315 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 = 3.381937315 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.381937315 + 2 x = 3.381937315 + 2 Combine like terms: 3.381937315 + 2 = 5.381937315 x = 5.381937315 Simplifying x = 5.381937315Subproblem 2
x + -2 = -3.381937315 Simplifying x + -2 = -3.381937315 Reorder the terms: -2 + x = -3.381937315 Solving -2 + x = -3.381937315 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 = -3.381937315 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.381937315 + 2 x = -3.381937315 + 2 Combine like terms: -3.381937315 + 2 = -1.381937315 x = -1.381937315 Simplifying x = -1.381937315Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.381937315, -1.381937315}
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