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Simplifying (2x2 + -5x + 27) + (3x2 + 7x + -74) = 0 Reorder the terms: (27 + -5x + 2x2) + (3x2 + 7x + -74) = 0 Remove parenthesis around (27 + -5x + 2x2) 27 + -5x + 2x2 + (3x2 + 7x + -74) = 0 Reorder the terms: 27 + -5x + 2x2 + (-74 + 7x + 3x2) = 0 Remove parenthesis around (-74 + 7x + 3x2) 27 + -5x + 2x2 + -74 + 7x + 3x2 = 0 Reorder the terms: 27 + -74 + -5x + 7x + 2x2 + 3x2 = 0 Combine like terms: 27 + -74 = -47 -47 + -5x + 7x + 2x2 + 3x2 = 0 Combine like terms: -5x + 7x = 2x -47 + 2x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 -47 + 2x + 5x2 = 0 Solving -47 + 2x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.4 + 0.4x + x2 = 0 Move the constant term to the right: Add '9.4' to each side of the equation. -9.4 + 0.4x + 9.4 + x2 = 0 + 9.4 Reorder the terms: -9.4 + 9.4 + 0.4x + x2 = 0 + 9.4 Combine like terms: -9.4 + 9.4 = 0.0 0.0 + 0.4x + x2 = 0 + 9.4 0.4x + x2 = 0 + 9.4 Combine like terms: 0 + 9.4 = 9.4 0.4x + x2 = 9.4 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 9.4 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 9.4 + 0.04 Combine like terms: 9.4 + 0.04 = 9.44 0.04 + 0.4x + x2 = 9.44 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 9.44 Calculate the square root of the right side: 3.072458299 Break this problem into two subproblems by setting (x + 0.2) equal to 3.072458299 and -3.072458299.Subproblem 1
x + 0.2 = 3.072458299 Simplifying x + 0.2 = 3.072458299 Reorder the terms: 0.2 + x = 3.072458299 Solving 0.2 + x = 3.072458299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 3.072458299 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 3.072458299 + -0.2 x = 3.072458299 + -0.2 Combine like terms: 3.072458299 + -0.2 = 2.872458299 x = 2.872458299 Simplifying x = 2.872458299Subproblem 2
x + 0.2 = -3.072458299 Simplifying x + 0.2 = -3.072458299 Reorder the terms: 0.2 + x = -3.072458299 Solving 0.2 + x = -3.072458299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -3.072458299 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -3.072458299 + -0.2 x = -3.072458299 + -0.2 Combine like terms: -3.072458299 + -0.2 = -3.272458299 x = -3.272458299 Simplifying x = -3.272458299Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.872458299, -3.272458299}
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