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Simplifying 50 = -16x2 + 32x + 48 Reorder the terms: 50 = 48 + 32x + -16x2 Solving 50 = 48 + 32x + -16x2 Solving for variable 'x'. Combine like terms: 50 + -48 = 2 2 + -32x + 16x2 = 48 + 32x + -16x2 + -48 + -32x + 16x2 Reorder the terms: 2 + -32x + 16x2 = 48 + -48 + 32x + -32x + -16x2 + 16x2 Combine like terms: 48 + -48 = 0 2 + -32x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2 2 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 2 + -32x + 16x2 = 0 + -16x2 + 16x2 2 + -32x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 2 + -32x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -16x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -16x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + -16x + 8x2 = 0 Solving 1 + -16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -2x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -2x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -2x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -2x + x2 = 0 + -0.125 -2x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -2x + x2 = -0.125 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.125 + 1 Reorder the terms: 1 + -2x + x2 = -0.125 + 1 Combine like terms: -0.125 + 1 = 0.875 1 + -2x + x2 = 0.875 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (x + -1) equal to 0.935414347 and -0.935414347.Subproblem 1
x + -1 = 0.935414347 Simplifying x + -1 = 0.935414347 Reorder the terms: -1 + x = 0.935414347 Solving -1 + x = 0.935414347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.935414347 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.935414347 + 1 x = 0.935414347 + 1 Combine like terms: 0.935414347 + 1 = 1.935414347 x = 1.935414347 Simplifying x = 1.935414347Subproblem 2
x + -1 = -0.935414347 Simplifying x + -1 = -0.935414347 Reorder the terms: -1 + x = -0.935414347 Solving -1 + x = -0.935414347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.935414347 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.935414347 + 1 x = -0.935414347 + 1 Combine like terms: -0.935414347 + 1 = 0.064585653 x = 0.064585653 Simplifying x = 0.064585653Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.935414347, 0.064585653}Solution
x = {1.935414347, 0.064585653}
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