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Simplifying (9 + -2x)(5 + -2x) = 24 Multiply (9 + -2x) * (5 + -2x) (9(5 + -2x) + -2x * (5 + -2x)) = 24 ((5 * 9 + -2x * 9) + -2x * (5 + -2x)) = 24 ((45 + -18x) + -2x * (5 + -2x)) = 24 (45 + -18x + (5 * -2x + -2x * -2x)) = 24 (45 + -18x + (-10x + 4x2)) = 24 Combine like terms: -18x + -10x = -28x (45 + -28x + 4x2) = 24 Solving 45 + -28x + 4x2 = 24 Solving for variable 'x'. Reorder the terms: 45 + -24 + -28x + 4x2 = 24 + -24 Combine like terms: 45 + -24 = 21 21 + -28x + 4x2 = 24 + -24 Combine like terms: 24 + -24 = 0 21 + -28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.25 + -7x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + -7x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + -7x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + -7x + x2 = 0 + -5.25 -7x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 -7x + x2 = -5.25 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -5.25 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -5.25 + 12.25 Combine like terms: -5.25 + 12.25 = 7 12.25 + -7x + x2 = 7 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -3.5) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -3.5 = 2.645751311 Simplifying x + -3.5 = 2.645751311 Reorder the terms: -3.5 + x = 2.645751311 Solving -3.5 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.645751311 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.645751311 + 3.5 x = 2.645751311 + 3.5 Combine like terms: 2.645751311 + 3.5 = 6.145751311 x = 6.145751311 Simplifying x = 6.145751311Subproblem 2
x + -3.5 = -2.645751311 Simplifying x + -3.5 = -2.645751311 Reorder the terms: -3.5 + x = -2.645751311 Solving -3.5 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.645751311 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.645751311 + 3.5 x = -2.645751311 + 3.5 Combine like terms: -2.645751311 + 3.5 = 0.854248689 x = 0.854248689 Simplifying x = 0.854248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.145751311, 0.854248689}
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