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Simplifying 0.5(x + 3)(x + -7) = 72 Reorder the terms: 0.5(3 + x)(x + -7) = 72 Reorder the terms: 0.5(3 + x)(-7 + x) = 72 Multiply (3 + x) * (-7 + x) 0.5(3(-7 + x) + x(-7 + x)) = 72 0.5((-7 * 3 + x * 3) + x(-7 + x)) = 72 0.5((-21 + 3x) + x(-7 + x)) = 72 0.5(-21 + 3x + (-7 * x + x * x)) = 72 0.5(-21 + 3x + (-7x + x2)) = 72 Combine like terms: 3x + -7x = -4x 0.5(-21 + -4x + x2) = 72 (-21 * 0.5 + -4x * 0.5 + x2 * 0.5) = 72 (-10.5 + -2x + 0.5x2) = 72 Solving -10.5 + -2x + 0.5x2 = 72 Solving for variable 'x'. Reorder the terms: -10.5 + -72 + -2x + 0.5x2 = 72 + -72 Combine like terms: -10.5 + -72 = -82.5 -82.5 + -2x + 0.5x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -82.5 + -2x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -165 + -4x + x2 = 0 Move the constant term to the right: Add '165' to each side of the equation. -165 + -4x + 165 + x2 = 0 + 165 Reorder the terms: -165 + 165 + -4x + x2 = 0 + 165 Combine like terms: -165 + 165 = 0 0 + -4x + x2 = 0 + 165 -4x + x2 = 0 + 165 Combine like terms: 0 + 165 = 165 -4x + x2 = 165 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 165 + 4 Reorder the terms: 4 + -4x + x2 = 165 + 4 Combine like terms: 165 + 4 = 169 4 + -4x + x2 = 169 Factor a perfect square on the left side: (x + -2)(x + -2) = 169 Calculate the square root of the right side: 13 Break this problem into two subproblems by setting (x + -2) equal to 13 and -13.Subproblem 1
x + -2 = 13 Simplifying x + -2 = 13 Reorder the terms: -2 + x = 13 Solving -2 + x = 13 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 13 + 2 Combine like terms: -2 + 2 = 0 0 + x = 13 + 2 x = 13 + 2 Combine like terms: 13 + 2 = 15 x = 15 Simplifying x = 15Subproblem 2
x + -2 = -13 Simplifying x + -2 = -13 Reorder the terms: -2 + x = -13 Solving -2 + x = -13 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -13 + 2 Combine like terms: -2 + 2 = 0 0 + x = -13 + 2 x = -13 + 2 Combine like terms: -13 + 2 = -11 x = -11 Simplifying x = -11Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, -11}
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