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Simplifying 9(4x + 2) * x = 5 Reorder the terms: 9(2 + 4x) * x = 5 Reorder the terms for easier multiplication: 9x(2 + 4x) = 5 (2 * 9x + 4x * 9x) = 5 (18x + 36x2) = 5 Solving 18x + 36x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 18x + 36x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 18x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.1388888889 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.1388888889' to each side of the equation. -0.1388888889 + 0.5x + 0.1388888889 + x2 = 0 + 0.1388888889 Reorder the terms: -0.1388888889 + 0.1388888889 + 0.5x + x2 = 0 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + 0.1388888889 0.5x + x2 = 0 + 0.1388888889 Combine like terms: 0 + 0.1388888889 = 0.1388888889 0.5x + x2 = 0.1388888889 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.1388888889 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.1388888889 + 0.0625 Combine like terms: 0.1388888889 + 0.0625 = 0.2013888889 0.0625 + 0.5x + x2 = 0.2013888889 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.2013888889 Calculate the square root of the right side: 0.448763734 Break this problem into two subproblems by setting (x + 0.25) equal to 0.448763734 and -0.448763734.Subproblem 1
x + 0.25 = 0.448763734 Simplifying x + 0.25 = 0.448763734 Reorder the terms: 0.25 + x = 0.448763734 Solving 0.25 + x = 0.448763734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.448763734 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.448763734 + -0.25 x = 0.448763734 + -0.25 Combine like terms: 0.448763734 + -0.25 = 0.198763734 x = 0.198763734 Simplifying x = 0.198763734Subproblem 2
x + 0.25 = -0.448763734 Simplifying x + 0.25 = -0.448763734 Reorder the terms: 0.25 + x = -0.448763734 Solving 0.25 + x = -0.448763734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.448763734 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.448763734 + -0.25 x = -0.448763734 + -0.25 Combine like terms: -0.448763734 + -0.25 = -0.698763734 x = -0.698763734 Simplifying x = -0.698763734Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.198763734, -0.698763734}
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