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Simplifying -16x2 + -10x + 200 = 0 Reorder the terms: 200 + -10x + -16x2 = 0 Solving 200 + -10x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(100 + -5x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(100 + -5x + -8x2)' equal to zero and attempt to solve: Simplifying 100 + -5x + -8x2 = 0 Solving 100 + -5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -12.5 + 0.625x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 0.625x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 0.625x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 0.625x + x2 = 0 + 12.5 0.625x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 0.625x + x2 = 12.5 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 12.5 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 12.5 + 0.09765625 Combine like terms: 12.5 + 0.09765625 = 12.59765625 0.09765625 + 0.625x + x2 = 12.59765625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 12.59765625 Calculate the square root of the right side: 3.549317716 Break this problem into two subproblems by setting (x + 0.3125) equal to 3.549317716 and -3.549317716.Subproblem 1
x + 0.3125 = 3.549317716 Simplifying x + 0.3125 = 3.549317716 Reorder the terms: 0.3125 + x = 3.549317716 Solving 0.3125 + x = 3.549317716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 3.549317716 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 3.549317716 + -0.3125 x = 3.549317716 + -0.3125 Combine like terms: 3.549317716 + -0.3125 = 3.236817716 x = 3.236817716 Simplifying x = 3.236817716Subproblem 2
x + 0.3125 = -3.549317716 Simplifying x + 0.3125 = -3.549317716 Reorder the terms: 0.3125 + x = -3.549317716 Solving 0.3125 + x = -3.549317716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -3.549317716 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -3.549317716 + -0.3125 x = -3.549317716 + -0.3125 Combine like terms: -3.549317716 + -0.3125 = -3.861817716 x = -3.861817716 Simplifying x = -3.861817716Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.236817716, -3.861817716}Solution
x = {3.236817716, -3.861817716}
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