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Simplifying (7x2 + 6x + 3) + -1(2x2 + -3x + 7) = 0 Reorder the terms: (3 + 6x + 7x2) + -1(2x2 + -3x + 7) = 0 Remove parenthesis around (3 + 6x + 7x2) 3 + 6x + 7x2 + -1(2x2 + -3x + 7) = 0 Reorder the terms: 3 + 6x + 7x2 + -1(7 + -3x + 2x2) = 0 3 + 6x + 7x2 + (7 * -1 + -3x * -1 + 2x2 * -1) = 0 3 + 6x + 7x2 + (-7 + 3x + -2x2) = 0 Reorder the terms: 3 + -7 + 6x + 3x + 7x2 + -2x2 = 0 Combine like terms: 3 + -7 = -4 -4 + 6x + 3x + 7x2 + -2x2 = 0 Combine like terms: 6x + 3x = 9x -4 + 9x + 7x2 + -2x2 = 0 Combine like terms: 7x2 + -2x2 = 5x2 -4 + 9x + 5x2 = 0 Solving -4 + 9x + 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'. -0.8 + 1.8x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 1.8x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 1.8x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 1.8x + x2 = 0 + 0.8 1.8x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 1.8x + x2 = 0.8 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 0.8 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.8 + 0.81 Combine like terms: 0.8 + 0.81 = 1.61 0.81 + 1.8x + x2 = 1.61 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (x + 0.9) equal to 1.268857754 and -1.268857754.Subproblem 1
x + 0.9 = 1.268857754 Simplifying x + 0.9 = 1.268857754 Reorder the terms: 0.9 + x = 1.268857754 Solving 0.9 + x = 1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 1.268857754 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.268857754 + -0.9 x = 1.268857754 + -0.9 Combine like terms: 1.268857754 + -0.9 = 0.368857754 x = 0.368857754 Simplifying x = 0.368857754Subproblem 2
x + 0.9 = -1.268857754 Simplifying x + 0.9 = -1.268857754 Reorder the terms: 0.9 + x = -1.268857754 Solving 0.9 + x = -1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -1.268857754 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.268857754 + -0.9 x = -1.268857754 + -0.9 Combine like terms: -1.268857754 + -0.9 = -2.168857754 x = -2.168857754 Simplifying x = -2.168857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.368857754, -2.168857754}
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