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Simplifying -16x2 + 10x + 448 = 0 Reorder the terms: 448 + 10x + -16x2 = 0 Solving 448 + 10x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(224 + 5x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(224 + 5x + -8x2)' equal to zero and attempt to solve: Simplifying 224 + 5x + -8x2 = 0 Solving 224 + 5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -28 + -0.625x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -0.625x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -0.625x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -0.625x + x2 = 0 + 28 -0.625x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -0.625x + x2 = 28 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 = 28 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 28 + 0.09765625 Combine like terms: 28 + 0.09765625 = 28.09765625 0.09765625 + -0.625x + x2 = 28.09765625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 28.09765625 Calculate the square root of the right side: 5.300722239 Break this problem into two subproblems by setting (x + -0.3125) equal to 5.300722239 and -5.300722239.Subproblem 1
x + -0.3125 = 5.300722239 Simplifying x + -0.3125 = 5.300722239 Reorder the terms: -0.3125 + x = 5.300722239 Solving -0.3125 + x = 5.300722239 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 = 5.300722239 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 5.300722239 + 0.3125 x = 5.300722239 + 0.3125 Combine like terms: 5.300722239 + 0.3125 = 5.613222239 x = 5.613222239 Simplifying x = 5.613222239Subproblem 2
x + -0.3125 = -5.300722239 Simplifying x + -0.3125 = -5.300722239 Reorder the terms: -0.3125 + x = -5.300722239 Solving -0.3125 + x = -5.300722239 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 = -5.300722239 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -5.300722239 + 0.3125 x = -5.300722239 + 0.3125 Combine like terms: -5.300722239 + 0.3125 = -4.988222239 x = -4.988222239 Simplifying x = -4.988222239Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.613222239, -4.988222239}Solution
x = {5.613222239, -4.988222239}
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