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Simplifying (3x2 + 7x + 1) + -1(8 + 5x + x2) = 0 Reorder the terms: (1 + 7x + 3x2) + -1(8 + 5x + x2) = 0 Remove parenthesis around (1 + 7x + 3x2) 1 + 7x + 3x2 + -1(8 + 5x + x2) = 0 1 + 7x + 3x2 + (8 * -1 + 5x * -1 + x2 * -1) = 0 1 + 7x + 3x2 + (-8 + -5x + -1x2) = 0 Reorder the terms: 1 + -8 + 7x + -5x + 3x2 + -1x2 = 0 Combine like terms: 1 + -8 = -7 -7 + 7x + -5x + 3x2 + -1x2 = 0 Combine like terms: 7x + -5x = 2x -7 + 2x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 -7 + 2x + 2x2 = 0 Solving -7 + 2x + 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'. -3.5 + x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x + x2 = 0 + 3.5 x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 x + x2 = 3.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 3.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 3.5 + 0.25 Combine like terms: 3.5 + 0.25 = 3.75 1.25 + x2 = 3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + 0.5) equal to 1.936491673 and -1.936491673.Subproblem 1
x + 0.5 = 1.936491673 Simplifying x + 0.5 = 1.936491673 Reorder the terms: 0.5 + x = 1.936491673 Solving 0.5 + x = 1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.936491673 + -0.5 x = 1.936491673 + -0.5 Combine like terms: 1.936491673 + -0.5 = 1.436491673 x = 1.436491673 Simplifying x = 1.436491673Subproblem 2
x + 0.5 = -1.936491673 Simplifying x + 0.5 = -1.936491673 Reorder the terms: 0.5 + x = -1.936491673 Solving 0.5 + x = -1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.936491673 + -0.5 x = -1.936491673 + -0.5 Combine like terms: -1.936491673 + -0.5 = -2.436491673 x = -2.436491673 Simplifying x = -2.436491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.436491673, -2.436491673}
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