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Simplifying 0.5(x + -5)(x + -15) = 0 Reorder the terms: 0.5(-5 + x)(x + -15) = 0 Reorder the terms: 0.5(-5 + x)(-15 + x) = 0 Multiply (-5 + x) * (-15 + x) 0.5(-5(-15 + x) + x(-15 + x)) = 0 0.5((-15 * -5 + x * -5) + x(-15 + x)) = 0 0.5((75 + -5x) + x(-15 + x)) = 0 0.5(75 + -5x + (-15 * x + x * x)) = 0 0.5(75 + -5x + (-15x + x2)) = 0 Combine like terms: -5x + -15x = -20x 0.5(75 + -20x + x2) = 0 (75 * 0.5 + -20x * 0.5 + x2 * 0.5) = 0 (37.5 + -10x + 0.5x2) = 0 Solving 37.5 + -10x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 75 + -20x + x2 = 0 Move the constant term to the right: Add '-75' to each side of the equation. 75 + -20x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -20x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -20x + x2 = 0 + -75 -20x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -20x + x2 = -75 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -75 + 100 Reorder the terms: 100 + -20x + x2 = -75 + 100 Combine like terms: -75 + 100 = 25 100 + -20x + x2 = 25 Factor a perfect square on the left side: (x + -10)(x + -10) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + -10) equal to 5 and -5.Subproblem 1
x + -10 = 5 Simplifying x + -10 = 5 Reorder the terms: -10 + x = 5 Solving -10 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 5 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5 + 10 x = 5 + 10 Combine like terms: 5 + 10 = 15 x = 15 Simplifying x = 15Subproblem 2
x + -10 = -5 Simplifying x + -10 = -5 Reorder the terms: -10 + x = -5 Solving -10 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -5 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5 + 10 x = -5 + 10 Combine like terms: -5 + 10 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, 5}
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