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Simplifying 44 = 0.5(x)(x + -3) Reorder the terms: 44 = 0.5x(-3 + x) 44 = (-3 * 0.5x + x * 0.5x) 44 = (-1.5x + 0.5x2) Solving 44 = -1.5x + 0.5x2 Solving for variable 'x'. Reorder the terms: 44 + 1.5x + -0.5x2 = -1.5x + 1.5x + 0.5x2 + -0.5x2 Combine like terms: -1.5x + 1.5x = 0.0 44 + 1.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2 44 + 1.5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 44 + 1.5x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -88 + -3x + x2 = 0 Move the constant term to the right: Add '88' to each side of the equation. -88 + -3x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + -3x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -3x + x2 = 0 + 88 -3x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 -3x + x2 = 88 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 = 88 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 88 + 2.25 Combine like terms: 88 + 2.25 = 90.25 2.25 + -3x + x2 = 90.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 90.25 Calculate the square root of the right side: 9.5 Break this problem into two subproblems by setting (x + -1.5) equal to 9.5 and -9.5.Subproblem 1
x + -1.5 = 9.5 Simplifying x + -1.5 = 9.5 Reorder the terms: -1.5 + x = 9.5 Solving -1.5 + x = 9.5 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 = 9.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 9.5 + 1.5 x = 9.5 + 1.5 Combine like terms: 9.5 + 1.5 = 11 x = 11 Simplifying x = 11Subproblem 2
x + -1.5 = -9.5 Simplifying x + -1.5 = -9.5 Reorder the terms: -1.5 + x = -9.5 Solving -1.5 + x = -9.5 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 = -9.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -9.5 + 1.5 x = -9.5 + 1.5 Combine like terms: -9.5 + 1.5 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {11, -8}
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