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Simplifying 16x2 + 128x + 100 = 0 Reorder the terms: 100 + 128x + 16x2 = 0 Solving 100 + 128x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 32x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + 32x + 4x2)' equal to zero and attempt to solve: Simplifying 25 + 32x + 4x2 = 0 Solving 25 + 32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + 8x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 8x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 8x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 8x + x2 = 0 + -6.25 8x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 8x + x2 = -6.25 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 = -6.25 + 16 Reorder the terms: 16 + 8x + x2 = -6.25 + 16 Combine like terms: -6.25 + 16 = 9.75 16 + 8x + x2 = 9.75 Factor a perfect square on the left side: (x + 4)(x + 4) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x + 4) equal to 3.122498999 and -3.122498999.Subproblem 1
x + 4 = 3.122498999 Simplifying x + 4 = 3.122498999 Reorder the terms: 4 + x = 3.122498999 Solving 4 + x = 3.122498999 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 = 3.122498999 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.122498999 + -4 x = 3.122498999 + -4 Combine like terms: 3.122498999 + -4 = -0.877501001 x = -0.877501001 Simplifying x = -0.877501001Subproblem 2
x + 4 = -3.122498999 Simplifying x + 4 = -3.122498999 Reorder the terms: 4 + x = -3.122498999 Solving 4 + x = -3.122498999 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 = -3.122498999 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.122498999 + -4 x = -3.122498999 + -4 Combine like terms: -3.122498999 + -4 = -7.122498999 x = -7.122498999 Simplifying x = -7.122498999Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.877501001, -7.122498999}Solution
x = {-0.877501001, -7.122498999}
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