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Simplifying -16x2 + 128x + 210 = 0 Reorder the terms: 210 + 128x + -16x2 = 0 Solving 210 + 128x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(105 + 64x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(105 + 64x + -8x2)' equal to zero and attempt to solve: Simplifying 105 + 64x + -8x2 = 0 Solving 105 + 64x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -13.125 + -8x + x2 = 0 Move the constant term to the right: Add '13.125' to each side of the equation. -13.125 + -8x + 13.125 + x2 = 0 + 13.125 Reorder the terms: -13.125 + 13.125 + -8x + x2 = 0 + 13.125 Combine like terms: -13.125 + 13.125 = 0.000 0.000 + -8x + x2 = 0 + 13.125 -8x + x2 = 0 + 13.125 Combine like terms: 0 + 13.125 = 13.125 -8x + x2 = 13.125 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 13.125 + 16 Reorder the terms: 16 + -8x + x2 = 13.125 + 16 Combine like terms: 13.125 + 16 = 29.125 16 + -8x + x2 = 29.125 Factor a perfect square on the left side: (x + -4)(x + -4) = 29.125 Calculate the square root of the right side: 5.396758286 Break this problem into two subproblems by setting (x + -4) equal to 5.396758286 and -5.396758286.Subproblem 1
x + -4 = 5.396758286 Simplifying x + -4 = 5.396758286 Reorder the terms: -4 + x = 5.396758286 Solving -4 + x = 5.396758286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.396758286 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.396758286 + 4 x = 5.396758286 + 4 Combine like terms: 5.396758286 + 4 = 9.396758286 x = 9.396758286 Simplifying x = 9.396758286Subproblem 2
x + -4 = -5.396758286 Simplifying x + -4 = -5.396758286 Reorder the terms: -4 + x = -5.396758286 Solving -4 + x = -5.396758286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.396758286 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.396758286 + 4 x = -5.396758286 + 4 Combine like terms: -5.396758286 + 4 = -1.396758286 x = -1.396758286 Simplifying x = -1.396758286Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.396758286, -1.396758286}Solution
x = {9.396758286, -1.396758286}
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