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Simplifying (3x2 + -5x + 4) + (7x2 + -1x + -9) = 0 Reorder the terms: (4 + -5x + 3x2) + (7x2 + -1x + -9) = 0 Remove parenthesis around (4 + -5x + 3x2) 4 + -5x + 3x2 + (7x2 + -1x + -9) = 0 Reorder the terms: 4 + -5x + 3x2 + (-9 + -1x + 7x2) = 0 Remove parenthesis around (-9 + -1x + 7x2) 4 + -5x + 3x2 + -9 + -1x + 7x2 = 0 Reorder the terms: 4 + -9 + -5x + -1x + 3x2 + 7x2 = 0 Combine like terms: 4 + -9 = -5 -5 + -5x + -1x + 3x2 + 7x2 = 0 Combine like terms: -5x + -1x = -6x -5 + -6x + 3x2 + 7x2 = 0 Combine like terms: 3x2 + 7x2 = 10x2 -5 + -6x + 10x2 = 0 Solving -5 + -6x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + -0.6x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.6x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.6x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.6x + x2 = 0.0 + 0.5 -0.6x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 -0.6x + x2 = 0.5 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 = 0.5 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.5 + 0.09 Combine like terms: 0.5 + 0.09 = 0.59 0.09 + -0.6x + x2 = 0.59 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.59 Calculate the square root of the right side: 0.768114575 Break this problem into two subproblems by setting (x + -0.3) equal to 0.768114575 and -0.768114575.Subproblem 1
x + -0.3 = 0.768114575 Simplifying x + -0.3 = 0.768114575 Reorder the terms: -0.3 + x = 0.768114575 Solving -0.3 + x = 0.768114575 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 = 0.768114575 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.768114575 + 0.3 x = 0.768114575 + 0.3 Combine like terms: 0.768114575 + 0.3 = 1.068114575 x = 1.068114575 Simplifying x = 1.068114575Subproblem 2
x + -0.3 = -0.768114575 Simplifying x + -0.3 = -0.768114575 Reorder the terms: -0.3 + x = -0.768114575 Solving -0.3 + x = -0.768114575 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 = -0.768114575 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.768114575 + 0.3 x = -0.768114575 + 0.3 Combine like terms: -0.768114575 + 0.3 = -0.468114575 x = -0.468114575 Simplifying x = -0.468114575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.068114575, -0.468114575}
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