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Simplifying -2.25(x + -1.5)(x + -6) = 0 Reorder the terms: -2.25(-1.5 + x)(x + -6) = 0 Reorder the terms: -2.25(-1.5 + x)(-6 + x) = 0 Multiply (-1.5 + x) * (-6 + x) -2.25(-1.5(-6 + x) + x(-6 + x)) = 0 -2.25((-6 * -1.5 + x * -1.5) + x(-6 + x)) = 0 -2.25((9 + -1.5x) + x(-6 + x)) = 0 -2.25(9 + -1.5x + (-6 * x + x * x)) = 0 -2.25(9 + -1.5x + (-6x + x2)) = 0 Combine like terms: -1.5x + -6x = -7.5x -2.25(9 + -7.5x + x2) = 0 (9 * -2.25 + -7.5x * -2.25 + x2 * -2.25) = 0 (-20.25 + 16.875x + -2.25x2) = 0 Solving -20.25 + 16.875x + -2.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.25 the coefficient of the squared term: Divide each side by '-2.25'. 9 + -7.5x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -7.5x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -7.5x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7.5x + x2 = 0 + -9 -7.5x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -7.5x + x2 = -9 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -9 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -9 + 14.0625 Combine like terms: -9 + 14.0625 = 5.0625 14.0625 + -7.5x + x2 = 5.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + -3.75) equal to 2.25 and -2.25.Subproblem 1
x + -3.75 = 2.25 Simplifying x + -3.75 = 2.25 Reorder the terms: -3.75 + x = 2.25 Solving -3.75 + x = 2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 2.25 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 2.25 + 3.75 x = 2.25 + 3.75 Combine like terms: 2.25 + 3.75 = 6 x = 6 Simplifying x = 6Subproblem 2
x + -3.75 = -2.25 Simplifying x + -3.75 = -2.25 Reorder the terms: -3.75 + x = -2.25 Solving -3.75 + x = -2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -2.25 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -2.25 + 3.75 x = -2.25 + 3.75 Combine like terms: -2.25 + 3.75 = 1.5 x = 1.5 Simplifying x = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, 1.5}
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