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Simplifying (2x2 + 3x + 7) + (3x2 + 6x + -19) = 0 Reorder the terms: (7 + 3x + 2x2) + (3x2 + 6x + -19) = 0 Remove parenthesis around (7 + 3x + 2x2) 7 + 3x + 2x2 + (3x2 + 6x + -19) = 0 Reorder the terms: 7 + 3x + 2x2 + (-19 + 6x + 3x2) = 0 Remove parenthesis around (-19 + 6x + 3x2) 7 + 3x + 2x2 + -19 + 6x + 3x2 = 0 Reorder the terms: 7 + -19 + 3x + 6x + 2x2 + 3x2 = 0 Combine like terms: 7 + -19 = -12 -12 + 3x + 6x + 2x2 + 3x2 = 0 Combine like terms: 3x + 6x = 9x -12 + 9x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 -12 + 9x + 5x2 = 0 Solving -12 + 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'. -2.4 + 1.8x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 1.8x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 1.8x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 1.8x + x2 = 0 + 2.4 1.8x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 1.8x + x2 = 2.4 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 = 2.4 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 2.4 + 0.81 Combine like terms: 2.4 + 0.81 = 3.21 0.81 + 1.8x + x2 = 3.21 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 3.21 Calculate the square root of the right side: 1.791647287 Break this problem into two subproblems by setting (x + 0.9) equal to 1.791647287 and -1.791647287.Subproblem 1
x + 0.9 = 1.791647287 Simplifying x + 0.9 = 1.791647287 Reorder the terms: 0.9 + x = 1.791647287 Solving 0.9 + x = 1.791647287 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 = 1.791647287 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.791647287 + -0.9 x = 1.791647287 + -0.9 Combine like terms: 1.791647287 + -0.9 = 0.891647287 x = 0.891647287 Simplifying x = 0.891647287Subproblem 2
x + 0.9 = -1.791647287 Simplifying x + 0.9 = -1.791647287 Reorder the terms: 0.9 + x = -1.791647287 Solving 0.9 + x = -1.791647287 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 = -1.791647287 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.791647287 + -0.9 x = -1.791647287 + -0.9 Combine like terms: -1.791647287 + -0.9 = -2.691647287 x = -2.691647287 Simplifying x = -2.691647287Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.891647287, -2.691647287}
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