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Simplifying 6x(5x + 4) = -1 Reorder the terms: 6x(4 + 5x) = -1 (4 * 6x + 5x * 6x) = -1 (24x + 30x2) = -1 Solving 24x + 30x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 24x + 30x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 24x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.03333333333 + 0.8x + x2 = 0.0 Move the constant term to the right: Add '-0.03333333333' to each side of the equation. 0.03333333333 + 0.8x + -0.03333333333 + x2 = 0.0 + -0.03333333333 Reorder the terms: 0.03333333333 + -0.03333333333 + 0.8x + x2 = 0.0 + -0.03333333333 Combine like terms: 0.03333333333 + -0.03333333333 = 0.00000000000 0.00000000000 + 0.8x + x2 = 0.0 + -0.03333333333 0.8x + x2 = 0.0 + -0.03333333333 Combine like terms: 0.0 + -0.03333333333 = -0.03333333333 0.8x + x2 = -0.03333333333 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = -0.03333333333 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = -0.03333333333 + 0.16 Combine like terms: -0.03333333333 + 0.16 = 0.12666666667 0.16 + 0.8x + x2 = 0.12666666667 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 0.12666666667 Calculate the square root of the right side: 0.355902608 Break this problem into two subproblems by setting (x + 0.4) equal to 0.355902608 and -0.355902608.Subproblem 1
x + 0.4 = 0.355902608 Simplifying x + 0.4 = 0.355902608 Reorder the terms: 0.4 + x = 0.355902608 Solving 0.4 + x = 0.355902608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 0.355902608 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.355902608 + -0.4 x = 0.355902608 + -0.4 Combine like terms: 0.355902608 + -0.4 = -0.044097392 x = -0.044097392 Simplifying x = -0.044097392Subproblem 2
x + 0.4 = -0.355902608 Simplifying x + 0.4 = -0.355902608 Reorder the terms: 0.4 + x = -0.355902608 Solving 0.4 + x = -0.355902608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -0.355902608 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.355902608 + -0.4 x = -0.355902608 + -0.4 Combine like terms: -0.355902608 + -0.4 = -0.755902608 x = -0.755902608 Simplifying x = -0.755902608Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.044097392, -0.755902608}
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