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Simplifying 16x2 + 32x = 166 Reorder the terms: 32x + 16x2 = 166 Solving 32x + 16x2 = 166 Solving for variable 'x'. Reorder the terms: -166 + 32x + 16x2 = 166 + -166 Combine like terms: 166 + -166 = 0 -166 + 32x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-83 + 16x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-83 + 16x + 8x2)' equal to zero and attempt to solve: Simplifying -83 + 16x + 8x2 = 0 Solving -83 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -10.375 + 2x + x2 = 0 Move the constant term to the right: Add '10.375' to each side of the equation. -10.375 + 2x + 10.375 + x2 = 0 + 10.375 Reorder the terms: -10.375 + 10.375 + 2x + x2 = 0 + 10.375 Combine like terms: -10.375 + 10.375 = 0.000 0.000 + 2x + x2 = 0 + 10.375 2x + x2 = 0 + 10.375 Combine like terms: 0 + 10.375 = 10.375 2x + x2 = 10.375 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 = 10.375 + 1 Reorder the terms: 1 + 2x + x2 = 10.375 + 1 Combine like terms: 10.375 + 1 = 11.375 1 + 2x + x2 = 11.375 Factor a perfect square on the left side: (x + 1)(x + 1) = 11.375 Calculate the square root of the right side: 3.372684391 Break this problem into two subproblems by setting (x + 1) equal to 3.372684391 and -3.372684391.Subproblem 1
x + 1 = 3.372684391 Simplifying x + 1 = 3.372684391 Reorder the terms: 1 + x = 3.372684391 Solving 1 + x = 3.372684391 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 = 3.372684391 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.372684391 + -1 x = 3.372684391 + -1 Combine like terms: 3.372684391 + -1 = 2.372684391 x = 2.372684391 Simplifying x = 2.372684391Subproblem 2
x + 1 = -3.372684391 Simplifying x + 1 = -3.372684391 Reorder the terms: 1 + x = -3.372684391 Solving 1 + x = -3.372684391 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 = -3.372684391 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.372684391 + -1 x = -3.372684391 + -1 Combine like terms: -3.372684391 + -1 = -4.372684391 x = -4.372684391 Simplifying x = -4.372684391Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.372684391, -4.372684391}Solution
x = {2.372684391, -4.372684391}
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