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Simplifying -16x2 + 64x + 192 = 1.5 Reorder the terms: 192 + 64x + -16x2 = 1.5 Solving 192 + 64x + -16x2 = 1.5 Solving for variable 'x'. Reorder the terms: 192 + -1.5 + 64x + -16x2 = 1.5 + -1.5 Combine like terms: 192 + -1.5 = 190.5 190.5 + 64x + -16x2 = 1.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 190.5 + 64x + -16x2 = 0.0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -11.90625 + -4x + x2 = 0.0 Move the constant term to the right: Add '11.90625' to each side of the equation. -11.90625 + -4x + 11.90625 + x2 = 0.0 + 11.90625 Reorder the terms: -11.90625 + 11.90625 + -4x + x2 = 0.0 + 11.90625 Combine like terms: -11.90625 + 11.90625 = 0.00000 0.00000 + -4x + x2 = 0.0 + 11.90625 -4x + x2 = 0.0 + 11.90625 Combine like terms: 0.0 + 11.90625 = 11.90625 -4x + x2 = 11.90625 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 = 11.90625 + 4 Reorder the terms: 4 + -4x + x2 = 11.90625 + 4 Combine like terms: 11.90625 + 4 = 15.90625 4 + -4x + x2 = 15.90625 Factor a perfect square on the left side: (x + -2)(x + -2) = 15.90625 Calculate the square root of the right side: 3.988264033 Break this problem into two subproblems by setting (x + -2) equal to 3.988264033 and -3.988264033.Subproblem 1
x + -2 = 3.988264033 Simplifying x + -2 = 3.988264033 Reorder the terms: -2 + x = 3.988264033 Solving -2 + x = 3.988264033 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 = 3.988264033 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.988264033 + 2 x = 3.988264033 + 2 Combine like terms: 3.988264033 + 2 = 5.988264033 x = 5.988264033 Simplifying x = 5.988264033Subproblem 2
x + -2 = -3.988264033 Simplifying x + -2 = -3.988264033 Reorder the terms: -2 + x = -3.988264033 Solving -2 + x = -3.988264033 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 = -3.988264033 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.988264033 + 2 x = -3.988264033 + 2 Combine like terms: -3.988264033 + 2 = -1.988264033 x = -1.988264033 Simplifying x = -1.988264033Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.988264033, -1.988264033}
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