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Simplifying (16x2 + -8x + 2) + (3x2 + -5x) = 0 Reorder the terms: (2 + -8x + 16x2) + (3x2 + -5x) = 0 Remove parenthesis around (2 + -8x + 16x2) 2 + -8x + 16x2 + (3x2 + -5x) = 0 Reorder the terms: 2 + -8x + 16x2 + (-5x + 3x2) = 0 Remove parenthesis around (-5x + 3x2) 2 + -8x + 16x2 + -5x + 3x2 = 0 Reorder the terms: 2 + -8x + -5x + 16x2 + 3x2 = 0 Combine like terms: -8x + -5x = -13x 2 + -13x + 16x2 + 3x2 = 0 Combine like terms: 16x2 + 3x2 = 19x2 2 + -13x + 19x2 = 0 Solving 2 + -13x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 0.1052631579 + -0.6842105263x + x2 = 0 Move the constant term to the right: Add '-0.1052631579' to each side of the equation. 0.1052631579 + -0.6842105263x + -0.1052631579 + x2 = 0 + -0.1052631579 Reorder the terms: 0.1052631579 + -0.1052631579 + -0.6842105263x + x2 = 0 + -0.1052631579 Combine like terms: 0.1052631579 + -0.1052631579 = 0.0000000000 0.0000000000 + -0.6842105263x + x2 = 0 + -0.1052631579 -0.6842105263x + x2 = 0 + -0.1052631579 Combine like terms: 0 + -0.1052631579 = -0.1052631579 -0.6842105263x + x2 = -0.1052631579 The x term is -0.6842105263x. Take half its coefficient (-0.3421052632). Square it (0.1170360111) and add it to both sides. Add '0.1170360111' to each side of the equation. -0.6842105263x + 0.1170360111 + x2 = -0.1052631579 + 0.1170360111 Reorder the terms: 0.1170360111 + -0.6842105263x + x2 = -0.1052631579 + 0.1170360111 Combine like terms: -0.1052631579 + 0.1170360111 = 0.0117728532 0.1170360111 + -0.6842105263x + x2 = 0.0117728532 Factor a perfect square on the left side: (x + -0.3421052632)(x + -0.3421052632) = 0.0117728532 Calculate the square root of the right side: 0.10850278 Break this problem into two subproblems by setting (x + -0.3421052632) equal to 0.10850278 and -0.10850278.Subproblem 1
x + -0.3421052632 = 0.10850278 Simplifying x + -0.3421052632 = 0.10850278 Reorder the terms: -0.3421052632 + x = 0.10850278 Solving -0.3421052632 + x = 0.10850278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3421052632' to each side of the equation. -0.3421052632 + 0.3421052632 + x = 0.10850278 + 0.3421052632 Combine like terms: -0.3421052632 + 0.3421052632 = 0.0000000000 0.0000000000 + x = 0.10850278 + 0.3421052632 x = 0.10850278 + 0.3421052632 Combine like terms: 0.10850278 + 0.3421052632 = 0.4506080432 x = 0.4506080432 Simplifying x = 0.4506080432Subproblem 2
x + -0.3421052632 = -0.10850278 Simplifying x + -0.3421052632 = -0.10850278 Reorder the terms: -0.3421052632 + x = -0.10850278 Solving -0.3421052632 + x = -0.10850278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3421052632' to each side of the equation. -0.3421052632 + 0.3421052632 + x = -0.10850278 + 0.3421052632 Combine like terms: -0.3421052632 + 0.3421052632 = 0.0000000000 0.0000000000 + x = -0.10850278 + 0.3421052632 x = -0.10850278 + 0.3421052632 Combine like terms: -0.10850278 + 0.3421052632 = 0.2336024832 x = 0.2336024832 Simplifying x = 0.2336024832Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4506080432, 0.2336024832}
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