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Simplifying 6x(5x + 6) = -1 Reorder the terms: 6x(6 + 5x) = -1 (6 * 6x + 5x * 6x) = -1 (36x + 30x2) = -1 Solving 36x + 30x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 36x + 30x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 36x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.03333333333 + 1.2x + x2 = 0.0 Move the constant term to the right: Add '-0.03333333333' to each side of the equation. 0.03333333333 + 1.2x + -0.03333333333 + x2 = 0.0 + -0.03333333333 Reorder the terms: 0.03333333333 + -0.03333333333 + 1.2x + x2 = 0.0 + -0.03333333333 Combine like terms: 0.03333333333 + -0.03333333333 = 0.00000000000 0.00000000000 + 1.2x + x2 = 0.0 + -0.03333333333 1.2x + x2 = 0.0 + -0.03333333333 Combine like terms: 0.0 + -0.03333333333 = -0.03333333333 1.2x + x2 = -0.03333333333 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = -0.03333333333 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -0.03333333333 + 0.36 Combine like terms: -0.03333333333 + 0.36 = 0.32666666667 0.36 + 1.2x + x2 = 0.32666666667 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.32666666667 Calculate the square root of the right side: 0.571547607 Break this problem into two subproblems by setting (x + 0.6) equal to 0.571547607 and -0.571547607.Subproblem 1
x + 0.6 = 0.571547607 Simplifying x + 0.6 = 0.571547607 Reorder the terms: 0.6 + x = 0.571547607 Solving 0.6 + x = 0.571547607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0.571547607 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.571547607 + -0.6 x = 0.571547607 + -0.6 Combine like terms: 0.571547607 + -0.6 = -0.028452393 x = -0.028452393 Simplifying x = -0.028452393Subproblem 2
x + 0.6 = -0.571547607 Simplifying x + 0.6 = -0.571547607 Reorder the terms: 0.6 + x = -0.571547607 Solving 0.6 + x = -0.571547607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -0.571547607 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.571547607 + -0.6 x = -0.571547607 + -0.6 Combine like terms: -0.571547607 + -0.6 = -1.171547607 x = -1.171547607 Simplifying x = -1.171547607Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.028452393, -1.171547607}
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