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Simplifying (x + 9) * x * 4 = 55 Reorder the terms: (9 + x) * x * 4 = 55 Reorder the terms for easier multiplication: 4x(9 + x) = 55 (9 * 4x + x * 4x) = 55 (36x + 4x2) = 55 Solving 36x + 4x2 = 55 Solving for variable 'x'. Reorder the terms: -55 + 36x + 4x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + 36x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.75 + 9x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + 9x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + 9x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + 9x + x2 = 0 + 13.75 9x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 9x + x2 = 13.75 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 13.75 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 13.75 + 20.25 Combine like terms: 13.75 + 20.25 = 34 20.25 + 9x + x2 = 34 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + 4.5) equal to 5.830951895 and -5.830951895.Subproblem 1
x + 4.5 = 5.830951895 Simplifying x + 4.5 = 5.830951895 Reorder the terms: 4.5 + x = 5.830951895 Solving 4.5 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.830951895 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.830951895 + -4.5 x = 5.830951895 + -4.5 Combine like terms: 5.830951895 + -4.5 = 1.330951895 x = 1.330951895 Simplifying x = 1.330951895Subproblem 2
x + 4.5 = -5.830951895 Simplifying x + 4.5 = -5.830951895 Reorder the terms: 4.5 + x = -5.830951895 Solving 4.5 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.830951895 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.830951895 + -4.5 x = -5.830951895 + -4.5 Combine like terms: -5.830951895 + -4.5 = -10.330951895 x = -10.330951895 Simplifying x = -10.330951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.330951895, -10.330951895}
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