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Simplifying 20x2 + -75x = -3x + 33 Reorder the terms: -75x + 20x2 = -3x + 33 Reorder the terms: -75x + 20x2 = 33 + -3x Solving -75x + 20x2 = 33 + -3x Solving for variable 'x'. Reorder the terms: -33 + -75x + 3x + 20x2 = 33 + -3x + -33 + 3x Combine like terms: -75x + 3x = -72x -33 + -72x + 20x2 = 33 + -3x + -33 + 3x Reorder the terms: -33 + -72x + 20x2 = 33 + -33 + -3x + 3x Combine like terms: 33 + -33 = 0 -33 + -72x + 20x2 = 0 + -3x + 3x -33 + -72x + 20x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -33 + -72x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.65 + -3.6x + x2 = 0 Move the constant term to the right: Add '1.65' to each side of the equation. -1.65 + -3.6x + 1.65 + x2 = 0 + 1.65 Reorder the terms: -1.65 + 1.65 + -3.6x + x2 = 0 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + -3.6x + x2 = 0 + 1.65 -3.6x + x2 = 0 + 1.65 Combine like terms: 0 + 1.65 = 1.65 -3.6x + x2 = 1.65 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = 1.65 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 1.65 + 3.24 Combine like terms: 1.65 + 3.24 = 4.89 3.24 + -3.6x + x2 = 4.89 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 4.89 Calculate the square root of the right side: 2.211334439 Break this problem into two subproblems by setting (x + -1.8) equal to 2.211334439 and -2.211334439.Subproblem 1
x + -1.8 = 2.211334439 Simplifying x + -1.8 = 2.211334439 Reorder the terms: -1.8 + x = 2.211334439 Solving -1.8 + x = 2.211334439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 2.211334439 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 2.211334439 + 1.8 x = 2.211334439 + 1.8 Combine like terms: 2.211334439 + 1.8 = 4.011334439 x = 4.011334439 Simplifying x = 4.011334439Subproblem 2
x + -1.8 = -2.211334439 Simplifying x + -1.8 = -2.211334439 Reorder the terms: -1.8 + x = -2.211334439 Solving -1.8 + x = -2.211334439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -2.211334439 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -2.211334439 + 1.8 x = -2.211334439 + 1.8 Combine like terms: -2.211334439 + 1.8 = -0.411334439 x = -0.411334439 Simplifying x = -0.411334439Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.011334439, -0.411334439}
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