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Simplifying (-0.6X2 + 19X) + -1(0.4X2 + -29X + 44) = 0 Reorder the terms: (19X + -0.6X2) + -1(0.4X2 + -29X + 44) = 0 Remove parenthesis around (19X + -0.6X2) 19X + -0.6X2 + -1(0.4X2 + -29X + 44) = 0 Reorder the terms: 19X + -0.6X2 + -1(44 + -29X + 0.4X2) = 0 19X + -0.6X2 + (44 * -1 + -29X * -1 + 0.4X2 * -1) = 0 19X + -0.6X2 + (-44 + 29X + -0.4X2) = 0 Reorder the terms: -44 + 19X + 29X + -0.6X2 + -0.4X2 = 0 Combine like terms: 19X + 29X = 48X -44 + 48X + -0.6X2 + -0.4X2 = 0 Combine like terms: -0.6X2 + -0.4X2 = -1X2 -44 + 48X + -1X2 = 0 Solving -44 + 48X + -1X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 44 + -48X + X2 = 0 Move the constant term to the right: Add '-44' to each side of the equation. 44 + -48X + -44 + X2 = 0 + -44 Reorder the terms: 44 + -44 + -48X + X2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -48X + X2 = 0 + -44 -48X + X2 = 0 + -44 Combine like terms: 0 + -44 = -44 -48X + X2 = -44 The X term is -48X. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48X + 576 + X2 = -44 + 576 Reorder the terms: 576 + -48X + X2 = -44 + 576 Combine like terms: -44 + 576 = 532 576 + -48X + X2 = 532 Factor a perfect square on the left side: (X + -24)(X + -24) = 532 Calculate the square root of the right side: 23.065125189 Break this problem into two subproblems by setting (X + -24) equal to 23.065125189 and -23.065125189.Subproblem 1
X + -24 = 23.065125189 Simplifying X + -24 = 23.065125189 Reorder the terms: -24 + X = 23.065125189 Solving -24 + X = 23.065125189 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + X = 23.065125189 + 24 Combine like terms: -24 + 24 = 0 0 + X = 23.065125189 + 24 X = 23.065125189 + 24 Combine like terms: 23.065125189 + 24 = 47.065125189 X = 47.065125189 Simplifying X = 47.065125189Subproblem 2
X + -24 = -23.065125189 Simplifying X + -24 = -23.065125189 Reorder the terms: -24 + X = -23.065125189 Solving -24 + X = -23.065125189 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + X = -23.065125189 + 24 Combine like terms: -24 + 24 = 0 0 + X = -23.065125189 + 24 X = -23.065125189 + 24 Combine like terms: -23.065125189 + 24 = 0.934874811 X = 0.934874811 Simplifying X = 0.934874811Solution
The solution to the problem is based on the solutions from the subproblems. X = {47.065125189, 0.934874811}
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