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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 = 7.272001873 x = 7.272001873 Simplifying x = 7.272001873Subproblem 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 = -1.272001873 x = -1.272001873 Simplifying x = -1.272001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.272001873, -1.272001873}
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