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Simplifying (0.5x + -3)(0.5x + -7) = 120 Reorder the terms: (-3 + 0.5x)(0.5x + -7) = 120 Reorder the terms: (-3 + 0.5x)(-7 + 0.5x) = 120 Multiply (-3 + 0.5x) * (-7 + 0.5x) (-3(-7 + 0.5x) + 0.5x * (-7 + 0.5x)) = 120 ((-7 * -3 + 0.5x * -3) + 0.5x * (-7 + 0.5x)) = 120 ((21 + -1.5x) + 0.5x * (-7 + 0.5x)) = 120 (21 + -1.5x + (-7 * 0.5x + 0.5x * 0.5x)) = 120 (21 + -1.5x + (-3.5x + 0.25x2)) = 120 Combine like terms: -1.5x + -3.5x = -5x (21 + -5x + 0.25x2) = 120 Solving 21 + -5x + 0.25x2 = 120 Solving for variable 'x'. Reorder the terms: 21 + -120 + -5x + 0.25x2 = 120 + -120 Combine like terms: 21 + -120 = -99 -99 + -5x + 0.25x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -99 + -5x + 0.25x2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -396 + -20x + x2 = 0 Move the constant term to the right: Add '396' to each side of the equation. -396 + -20x + 396 + x2 = 0 + 396 Reorder the terms: -396 + 396 + -20x + x2 = 0 + 396 Combine like terms: -396 + 396 = 0 0 + -20x + x2 = 0 + 396 -20x + x2 = 0 + 396 Combine like terms: 0 + 396 = 396 -20x + x2 = 396 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 = 396 + 100 Reorder the terms: 100 + -20x + x2 = 396 + 100 Combine like terms: 396 + 100 = 496 100 + -20x + x2 = 496 Factor a perfect square on the left side: (x + -10)(x + -10) = 496 Calculate the square root of the right side: 22.271057451 Break this problem into two subproblems by setting (x + -10) equal to 22.271057451 and -22.271057451.Subproblem 1
x + -10 = 22.271057451 Simplifying x + -10 = 22.271057451 Reorder the terms: -10 + x = 22.271057451 Solving -10 + x = 22.271057451 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 = 22.271057451 + 10 Combine like terms: -10 + 10 = 0 0 + x = 22.271057451 + 10 x = 22.271057451 + 10 Combine like terms: 22.271057451 + 10 = 32.271057451 x = 32.271057451 Simplifying x = 32.271057451Subproblem 2
x + -10 = -22.271057451 Simplifying x + -10 = -22.271057451 Reorder the terms: -10 + x = -22.271057451 Solving -10 + x = -22.271057451 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 = -22.271057451 + 10 Combine like terms: -10 + 10 = 0 0 + x = -22.271057451 + 10 x = -22.271057451 + 10 Combine like terms: -22.271057451 + 10 = -12.271057451 x = -12.271057451 Simplifying x = -12.271057451Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.271057451, -12.271057451}
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