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Simplifying 16x + 4x(9x + 34) = 32 Reorder the terms: 16x + 4x(34 + 9x) = 32 16x + (34 * 4x + 9x * 4x) = 32 16x + (136x + 36x2) = 32 Combine like terms: 16x + 136x = 152x 152x + 36x2 = 32 Solving 152x + 36x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 152x + 36x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 152x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 38x + 9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + 38x + 9x2)' equal to zero and attempt to solve: Simplifying -8 + 38x + 9x2 = 0 Solving -8 + 38x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + 4.222222222x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 4.222222222x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 4.222222222x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 4.222222222x + x2 = 0 + 0.8888888889 4.222222222x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 4.222222222x + x2 = 0.8888888889 The x term is 4.222222222x. Take half its coefficient (2.111111111). Square it (4.456790123) and add it to both sides. Add '4.456790123' to each side of the equation. 4.222222222x + 4.456790123 + x2 = 0.8888888889 + 4.456790123 Reorder the terms: 4.456790123 + 4.222222222x + x2 = 0.8888888889 + 4.456790123 Combine like terms: 0.8888888889 + 4.456790123 = 5.3456790119 4.456790123 + 4.222222222x + x2 = 5.3456790119 Factor a perfect square on the left side: (x + 2.111111111)(x + 2.111111111) = 5.3456790119 Calculate the square root of the right side: 2.31207245 Break this problem into two subproblems by setting (x + 2.111111111) equal to 2.31207245 and -2.31207245.Subproblem 1
x + 2.111111111 = 2.31207245 Simplifying x + 2.111111111 = 2.31207245 Reorder the terms: 2.111111111 + x = 2.31207245 Solving 2.111111111 + x = 2.31207245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.111111111' to each side of the equation. 2.111111111 + -2.111111111 + x = 2.31207245 + -2.111111111 Combine like terms: 2.111111111 + -2.111111111 = 0.000000000 0.000000000 + x = 2.31207245 + -2.111111111 x = 2.31207245 + -2.111111111 Combine like terms: 2.31207245 + -2.111111111 = 0.200961339 x = 0.200961339 Simplifying x = 0.200961339Subproblem 2
x + 2.111111111 = -2.31207245 Simplifying x + 2.111111111 = -2.31207245 Reorder the terms: 2.111111111 + x = -2.31207245 Solving 2.111111111 + x = -2.31207245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.111111111' to each side of the equation. 2.111111111 + -2.111111111 + x = -2.31207245 + -2.111111111 Combine like terms: 2.111111111 + -2.111111111 = 0.000000000 0.000000000 + x = -2.31207245 + -2.111111111 x = -2.31207245 + -2.111111111 Combine like terms: -2.31207245 + -2.111111111 = -4.423183561 x = -4.423183561 Simplifying x = -4.423183561Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.200961339, -4.423183561}Solution
x = {0.200961339, -4.423183561}
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