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Simplifying (x2 + 3x + -5) + (-3x2 + -8x + 9) = 0 Reorder the terms: (-5 + 3x + x2) + (-3x2 + -8x + 9) = 0 Remove parenthesis around (-5 + 3x + x2) -5 + 3x + x2 + (-3x2 + -8x + 9) = 0 Reorder the terms: -5 + 3x + x2 + (9 + -8x + -3x2) = 0 Remove parenthesis around (9 + -8x + -3x2) -5 + 3x + x2 + 9 + -8x + -3x2 = 0 Reorder the terms: -5 + 9 + 3x + -8x + x2 + -3x2 = 0 Combine like terms: -5 + 9 = 4 4 + 3x + -8x + x2 + -3x2 = 0 Combine like terms: 3x + -8x = -5x 4 + -5x + x2 + -3x2 = 0 Combine like terms: x2 + -3x2 = -2x2 4 + -5x + -2x2 = 0 Solving 4 + -5x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2 + 2.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.5x + x2 = 0 + 2 2.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.5x + x2 = 2 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 2 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 2 + 1.5625 Combine like terms: 2 + 1.5625 = 3.5625 1.5625 + 2.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + 1.25) equal to 1.887458609 and -1.887458609.Subproblem 1
x + 1.25 = 1.887458609 Simplifying x + 1.25 = 1.887458609 Reorder the terms: 1.25 + x = 1.887458609 Solving 1.25 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.887458609 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.887458609 + -1.25 x = 1.887458609 + -1.25 Combine like terms: 1.887458609 + -1.25 = 0.637458609 x = 0.637458609 Simplifying x = 0.637458609Subproblem 2
x + 1.25 = -1.887458609 Simplifying x + 1.25 = -1.887458609 Reorder the terms: 1.25 + x = -1.887458609 Solving 1.25 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.887458609 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.887458609 + -1.25 x = -1.887458609 + -1.25 Combine like terms: -1.887458609 + -1.25 = -3.137458609 x = -3.137458609 Simplifying x = -3.137458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.637458609, -3.137458609}
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