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Simplifying 2(x + -4)(x + -6) = 73 Reorder the terms: 2(-4 + x)(x + -6) = 73 Reorder the terms: 2(-4 + x)(-6 + x) = 73 Multiply (-4 + x) * (-6 + x) 2(-4(-6 + x) + x(-6 + x)) = 73 2((-6 * -4 + x * -4) + x(-6 + x)) = 73 2((24 + -4x) + x(-6 + x)) = 73 2(24 + -4x + (-6 * x + x * x)) = 73 2(24 + -4x + (-6x + x2)) = 73 Combine like terms: -4x + -6x = -10x 2(24 + -10x + x2) = 73 (24 * 2 + -10x * 2 + x2 * 2) = 73 (48 + -20x + 2x2) = 73 Solving 48 + -20x + 2x2 = 73 Solving for variable 'x'. Reorder the terms: 48 + -73 + -20x + 2x2 = 73 + -73 Combine like terms: 48 + -73 = -25 -25 + -20x + 2x2 = 73 + -73 Combine like terms: 73 + -73 = 0 -25 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -10x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -10x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -10x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -10x + x2 = 0 + 12.5 -10x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -10x + x2 = 12.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 12.5 + 25 Reorder the terms: 25 + -10x + x2 = 12.5 + 25 Combine like terms: 12.5 + 25 = 37.5 25 + -10x + x2 = 37.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 37.5 Calculate the square root of the right side: 6.123724357 Break this problem into two subproblems by setting (x + -5) equal to 6.123724357 and -6.123724357.Subproblem 1
x + -5 = 6.123724357 Simplifying x + -5 = 6.123724357 Reorder the terms: -5 + x = 6.123724357 Solving -5 + x = 6.123724357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.123724357 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.123724357 + 5 x = 6.123724357 + 5 Combine like terms: 6.123724357 + 5 = 11.123724357 x = 11.123724357 Simplifying x = 11.123724357Subproblem 2
x + -5 = -6.123724357 Simplifying x + -5 = -6.123724357 Reorder the terms: -5 + x = -6.123724357 Solving -5 + x = -6.123724357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.123724357 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.123724357 + 5 x = -6.123724357 + 5 Combine like terms: -6.123724357 + 5 = -1.123724357 x = -1.123724357 Simplifying x = -1.123724357Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.123724357, -1.123724357}
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