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Simplifying (5 + 2x)(7 + 2x) = 72 Multiply (5 + 2x) * (7 + 2x) (5(7 + 2x) + 2x * (7 + 2x)) = 72 ((7 * 5 + 2x * 5) + 2x * (7 + 2x)) = 72 ((35 + 10x) + 2x * (7 + 2x)) = 72 (35 + 10x + (7 * 2x + 2x * 2x)) = 72 (35 + 10x + (14x + 4x2)) = 72 Combine like terms: 10x + 14x = 24x (35 + 24x + 4x2) = 72 Solving 35 + 24x + 4x2 = 72 Solving for variable 'x'. Reorder the terms: 35 + -72 + 24x + 4x2 = 72 + -72 Combine like terms: 35 + -72 = -37 -37 + 24x + 4x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -37 + 24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.25 + 6x + x2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + 6x + 9.25 + x2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + 6x + x2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + 6x + x2 = 0 + 9.25 6x + x2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 6x + x2 = 9.25 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 9.25 + 9 Reorder the terms: 9 + 6x + x2 = 9.25 + 9 Combine like terms: 9.25 + 9 = 18.25 9 + 6x + x2 = 18.25 Factor a perfect square on the left side: (x + 3)(x + 3) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + 3) equal to 4.272001873 and -4.272001873.Subproblem 1
x + 3 = 4.272001873 Simplifying x + 3 = 4.272001873 Reorder the terms: 3 + x = 4.272001873 Solving 3 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.272001873 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.272001873 + -3 x = 4.272001873 + -3 Combine like terms: 4.272001873 + -3 = 1.272001873 x = 1.272001873 Simplifying x = 1.272001873Subproblem 2
x + 3 = -4.272001873 Simplifying x + 3 = -4.272001873 Reorder the terms: 3 + x = -4.272001873 Solving 3 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.272001873 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.272001873 + -3 x = -4.272001873 + -3 Combine like terms: -4.272001873 + -3 = -7.272001873 x = -7.272001873 Simplifying x = -7.272001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.272001873, -7.272001873}
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