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Simplifying (x + 6) * 5x + 7 = 0 Reorder the terms: (6 + x) * 5x + 7 = 0 Reorder the terms for easier multiplication: 5x(6 + x) + 7 = 0 (6 * 5x + x * 5x) + 7 = 0 (30x + 5x2) + 7 = 0 Reorder the terms: 7 + 30x + 5x2 = 0 Solving 7 + 30x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 6x + x2 = 0 + -1.4 6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 6x + x2 = -1.4 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -1.4 + 9 Reorder the terms: 9 + 6x + x2 = -1.4 + 9 Combine like terms: -1.4 + 9 = 7.6 9 + 6x + x2 = 7.6 Factor a perfect square on the left side: (x + 3)(x + 3) = 7.6 Calculate the square root of the right side: 2.75680975 Break this problem into two subproblems by setting (x + 3) equal to 2.75680975 and -2.75680975.Subproblem 1
x + 3 = 2.75680975 Simplifying x + 3 = 2.75680975 Reorder the terms: 3 + x = 2.75680975 Solving 3 + x = 2.75680975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.75680975 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.75680975 + -3 x = 2.75680975 + -3 Combine like terms: 2.75680975 + -3 = -0.24319025 x = -0.24319025 Simplifying x = -0.24319025Subproblem 2
x + 3 = -2.75680975 Simplifying x + 3 = -2.75680975 Reorder the terms: 3 + x = -2.75680975 Solving 3 + x = -2.75680975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.75680975 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.75680975 + -3 x = -2.75680975 + -3 Combine like terms: -2.75680975 + -3 = -5.75680975 x = -5.75680975 Simplifying x = -5.75680975Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.24319025, -5.75680975}
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