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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 = 3x -12 + 3x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 -12 + 3x + 5x2 = 0 Solving -12 + 3x + 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 + 0.6x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 0.6x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 0.6x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 0.6x + x2 = 0 + 2.4 0.6x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 0.6x + x2 = 2.4 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 2.4 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 2.4 + 0.09 Combine like terms: 2.4 + 0.09 = 2.49 0.09 + 0.6x + x2 = 2.49 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 2.49 Calculate the square root of the right side: 1.577973384 Break this problem into two subproblems by setting (x + 0.3) equal to 1.577973384 and -1.577973384.Subproblem 1
x + 0.3 = 1.577973384 Simplifying x + 0.3 = 1.577973384 Reorder the terms: 0.3 + x = 1.577973384 Solving 0.3 + x = 1.577973384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1.577973384 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.577973384 + -0.3 x = 1.577973384 + -0.3 Combine like terms: 1.577973384 + -0.3 = 1.277973384 x = 1.277973384 Simplifying x = 1.277973384Subproblem 2
x + 0.3 = -1.577973384 Simplifying x + 0.3 = -1.577973384 Reorder the terms: 0.3 + x = -1.577973384 Solving 0.3 + x = -1.577973384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1.577973384 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.577973384 + -0.3 x = -1.577973384 + -0.3 Combine like terms: -1.577973384 + -0.3 = -1.877973384 x = -1.877973384 Simplifying x = -1.877973384Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.277973384, -1.877973384}
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