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Simplifying 5x(6) * x + 148x + 9x + 17 = 0 Reorder the terms for easier multiplication: 5 * 6x * x + 148x + 9x + 17 = 0 Multiply 5 * 6 30x * x + 148x + 9x + 17 = 0 Multiply x * x 30x2 + 148x + 9x + 17 = 0 Reorder the terms: 17 + 148x + 9x + 30x2 = 0 Combine like terms: 148x + 9x = 157x 17 + 157x + 30x2 = 0 Solving 17 + 157x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.5666666667 + 5.233333333x + x2 = 0.0 Move the constant term to the right: Add '-0.5666666667' to each side of the equation. 0.5666666667 + 5.233333333x + -0.5666666667 + x2 = 0.0 + -0.5666666667 Reorder the terms: 0.5666666667 + -0.5666666667 + 5.233333333x + x2 = 0.0 + -0.5666666667 Combine like terms: 0.5666666667 + -0.5666666667 = 0.0000000000 0.0000000000 + 5.233333333x + x2 = 0.0 + -0.5666666667 5.233333333x + x2 = 0.0 + -0.5666666667 Combine like terms: 0.0 + -0.5666666667 = -0.5666666667 5.233333333x + x2 = -0.5666666667 The x term is 5.233333333x. Take half its coefficient (2.616666667). Square it (6.846944446) and add it to both sides. Add '6.846944446' to each side of the equation. 5.233333333x + 6.846944446 + x2 = -0.5666666667 + 6.846944446 Reorder the terms: 6.846944446 + 5.233333333x + x2 = -0.5666666667 + 6.846944446 Combine like terms: -0.5666666667 + 6.846944446 = 6.2802777793 6.846944446 + 5.233333333x + x2 = 6.2802777793 Factor a perfect square on the left side: (x + 2.616666667)(x + 2.616666667) = 6.2802777793 Calculate the square root of the right side: 2.50604824 Break this problem into two subproblems by setting (x + 2.616666667) equal to 2.50604824 and -2.50604824.Subproblem 1
x + 2.616666667 = 2.50604824 Simplifying x + 2.616666667 = 2.50604824 Reorder the terms: 2.616666667 + x = 2.50604824 Solving 2.616666667 + x = 2.50604824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.616666667' to each side of the equation. 2.616666667 + -2.616666667 + x = 2.50604824 + -2.616666667 Combine like terms: 2.616666667 + -2.616666667 = 0.000000000 0.000000000 + x = 2.50604824 + -2.616666667 x = 2.50604824 + -2.616666667 Combine like terms: 2.50604824 + -2.616666667 = -0.110618427 x = -0.110618427 Simplifying x = -0.110618427Subproblem 2
x + 2.616666667 = -2.50604824 Simplifying x + 2.616666667 = -2.50604824 Reorder the terms: 2.616666667 + x = -2.50604824 Solving 2.616666667 + x = -2.50604824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.616666667' to each side of the equation. 2.616666667 + -2.616666667 + x = -2.50604824 + -2.616666667 Combine like terms: 2.616666667 + -2.616666667 = 0.000000000 0.000000000 + x = -2.50604824 + -2.616666667 x = -2.50604824 + -2.616666667 Combine like terms: -2.50604824 + -2.616666667 = -5.122714907 x = -5.122714907 Simplifying x = -5.122714907Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.110618427, -5.122714907}
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