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Simplifying 29 + 3(2 + 9x) * 1x(3 + 2) = 1x + 9(2 + 3x) + -1(2 + 1x) + -2 Combine like terms: 3 + 2 = 5 29 + 3(2 + 9x) * 1x(5) = 1x + 9(2 + 3x) + -1(2 + 1x) + -2 Reorder the terms for easier multiplication: 29 + 3 * 1 * 5x(2 + 9x) = 1x + 9(2 + 3x) + -1(2 + 1x) + -2 Multiply 3 * 1 29 + 3 * 5x(2 + 9x) = 1x + 9(2 + 3x) + -1(2 + 1x) + -2 Multiply 3 * 5 29 + 15x(2 + 9x) = 1x + 9(2 + 3x) + -1(2 + 1x) + -2 29 + (2 * 15x + 9x * 15x) = 1x + 9(2 + 3x) + -1(2 + 1x) + -2 29 + (30x + 135x2) = 1x + 9(2 + 3x) + -1(2 + 1x) + -2 29 + 30x + 135x2 = 1x + (2 * 9 + 3x * 9) + -1(2 + 1x) + -2 29 + 30x + 135x2 = 1x + (18 + 27x) + -1(2 + 1x) + -2 29 + 30x + 135x2 = 1x + 18 + 27x + (2 * -1 + 1x * -1) + -2 29 + 30x + 135x2 = 1x + 18 + 27x + (-2 + -1x) + -2 Reorder the terms: 29 + 30x + 135x2 = 18 + -2 + -2 + 1x + 27x + -1x Combine like terms: 18 + -2 = 16 29 + 30x + 135x2 = 16 + -2 + 1x + 27x + -1x Combine like terms: 16 + -2 = 14 29 + 30x + 135x2 = 14 + 1x + 27x + -1x Combine like terms: 1x + 27x = 28x 29 + 30x + 135x2 = 14 + 28x + -1x Combine like terms: 28x + -1x = 27x 29 + 30x + 135x2 = 14 + 27x Solving 29 + 30x + 135x2 = 14 + 27x Solving for variable 'x'. Reorder the terms: 29 + -14 + 30x + -27x + 135x2 = 14 + 27x + -14 + -27x Combine like terms: 29 + -14 = 15 15 + 30x + -27x + 135x2 = 14 + 27x + -14 + -27x Combine like terms: 30x + -27x = 3x 15 + 3x + 135x2 = 14 + 27x + -14 + -27x Reorder the terms: 15 + 3x + 135x2 = 14 + -14 + 27x + -27x Combine like terms: 14 + -14 = 0 15 + 3x + 135x2 = 0 + 27x + -27x 15 + 3x + 135x2 = 27x + -27x Combine like terms: 27x + -27x = 0 15 + 3x + 135x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + x + 45x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + x + 45x2)' equal to zero and attempt to solve: Simplifying 5 + x + 45x2 = 0 Solving 5 + x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. 0.1111111111 + 0.02222222222x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 0.02222222222x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 0.02222222222x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 0.02222222222x + x2 = 0 + -0.1111111111 0.02222222222x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 0.02222222222x + x2 = -0.1111111111 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.02222222222x + 0.25 + x2 = -0.1111111111 + 0.25 Reorder the terms: 0.25 + 0.02222222222x + x2 = -0.1111111111 + 0.25 Combine like terms: -0.1111111111 + 0.25 = 0.1388888889 0.25 + 0.02222222222x + x2 = 0.1388888889 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.1388888889 Calculate the square root of the right side: 0.372677996 Break this problem into two subproblems by setting (x + 0.5) equal to 0.372677996 and -0.372677996.Subproblem 1
x + 0.5 = 0.372677996 Simplifying x + 0.5 = 0.372677996 Reorder the terms: 0.5 + x = 0.372677996 Solving 0.5 + x = 0.372677996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.372677996 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.372677996 + -0.5 x = 0.372677996 + -0.5 Combine like terms: 0.372677996 + -0.5 = -0.127322004 x = -0.127322004 Simplifying x = -0.127322004Subproblem 2
x + 0.5 = -0.372677996 Simplifying x + 0.5 = -0.372677996 Reorder the terms: 0.5 + x = -0.372677996 Solving 0.5 + x = -0.372677996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.372677996 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.372677996 + -0.5 x = -0.372677996 + -0.5 Combine like terms: -0.372677996 + -0.5 = -0.872677996 x = -0.872677996 Simplifying x = -0.872677996Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.127322004, -0.872677996}Solution
x = {-0.127322004, -0.872677996}
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