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Simplifying 44 = x(x + -1.5) Reorder the terms: 44 = x(-1.5 + x) 44 = (-1.5 * x + x * x) 44 = (-1.5x + x2) Solving 44 = -1.5x + x2 Solving for variable 'x'. Reorder the terms: 44 + 1.5x + -1x2 = -1.5x + 1.5x + x2 + -1x2 Combine like terms: -1.5x + 1.5x = 0.0 44 + 1.5x + -1x2 = 0.0 + x2 + -1x2 44 + 1.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 44 + 1.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -44 + -1.5x + x2 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + -1.5x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -1.5x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -1.5x + x2 = 0 + 44 -1.5x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -1.5x + x2 = 44 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 44 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 44 + 0.5625 Combine like terms: 44 + 0.5625 = 44.5625 0.5625 + -1.5x + x2 = 44.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 44.5625 Calculate the square root of the right side: 6.675514961 Break this problem into two subproblems by setting (x + -0.75) equal to 6.675514961 and -6.675514961.Subproblem 1
x + -0.75 = 6.675514961 Simplifying x + -0.75 = 6.675514961 Reorder the terms: -0.75 + x = 6.675514961 Solving -0.75 + x = 6.675514961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 6.675514961 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 6.675514961 + 0.75 x = 6.675514961 + 0.75 Combine like terms: 6.675514961 + 0.75 = 7.425514961 x = 7.425514961 Simplifying x = 7.425514961Subproblem 2
x + -0.75 = -6.675514961 Simplifying x + -0.75 = -6.675514961 Reorder the terms: -0.75 + x = -6.675514961 Solving -0.75 + x = -6.675514961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -6.675514961 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -6.675514961 + 0.75 x = -6.675514961 + 0.75 Combine like terms: -6.675514961 + 0.75 = -5.925514961 x = -5.925514961 Simplifying x = -5.925514961Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.425514961, -5.925514961}
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