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Simplifying (0.5)(x)(x + -3) = 20 Reorder the terms: 0.5x(-3 + x) = 20 (-3 * 0.5x + x * 0.5x) = 20 (-1.5x + 0.5x2) = 20 Solving -1.5x + 0.5x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -1.5x + 0.5x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -1.5x + 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'. -40 + -3x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -3x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -3x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -3x + x2 = 0 + 40 -3x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -3x + x2 = 40 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 40 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 40 + 2.25 Combine like terms: 40 + 2.25 = 42.25 2.25 + -3x + x2 = 42.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 42.25 Calculate the square root of the right side: 6.5 Break this problem into two subproblems by setting (x + -1.5) equal to 6.5 and -6.5.Subproblem 1
x + -1.5 = 6.5 Simplifying x + -1.5 = 6.5 Reorder the terms: -1.5 + x = 6.5 Solving -1.5 + x = 6.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.5 + 1.5 x = 6.5 + 1.5 Combine like terms: 6.5 + 1.5 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -1.5 = -6.5 Simplifying x + -1.5 = -6.5 Reorder the terms: -1.5 + x = -6.5 Solving -1.5 + x = -6.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.5 + 1.5 x = -6.5 + 1.5 Combine like terms: -6.5 + 1.5 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -5}
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