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Simplifying 5x(x + 7) = 6(x + -5) Reorder the terms: 5x(7 + x) = 6(x + -5) (7 * 5x + x * 5x) = 6(x + -5) (35x + 5x2) = 6(x + -5) Reorder the terms: 35x + 5x2 = 6(-5 + x) 35x + 5x2 = (-5 * 6 + x * 6) 35x + 5x2 = (-30 + 6x) Solving 35x + 5x2 = -30 + 6x Solving for variable 'x'. Reorder the terms: 30 + 35x + -6x + 5x2 = -30 + 6x + 30 + -6x Combine like terms: 35x + -6x = 29x 30 + 29x + 5x2 = -30 + 6x + 30 + -6x Reorder the terms: 30 + 29x + 5x2 = -30 + 30 + 6x + -6x Combine like terms: -30 + 30 = 0 30 + 29x + 5x2 = 0 + 6x + -6x 30 + 29x + 5x2 = 6x + -6x Combine like terms: 6x + -6x = 0 30 + 29x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6 + 5.8x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 5.8x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 5.8x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5.8x + x2 = 0 + -6 5.8x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 5.8x + x2 = -6 The x term is 5.8x. Take half its coefficient (2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. 5.8x + 8.41 + x2 = -6 + 8.41 Reorder the terms: 8.41 + 5.8x + x2 = -6 + 8.41 Combine like terms: -6 + 8.41 = 2.41 8.41 + 5.8x + x2 = 2.41 Factor a perfect square on the left side: (x + 2.9)(x + 2.9) = 2.41 Calculate the square root of the right side: 1.55241747 Break this problem into two subproblems by setting (x + 2.9) equal to 1.55241747 and -1.55241747.Subproblem 1
x + 2.9 = 1.55241747 Simplifying x + 2.9 = 1.55241747 Reorder the terms: 2.9 + x = 1.55241747 Solving 2.9 + x = 1.55241747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + x = 1.55241747 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + x = 1.55241747 + -2.9 x = 1.55241747 + -2.9 Combine like terms: 1.55241747 + -2.9 = -1.34758253 x = -1.34758253 Simplifying x = -1.34758253Subproblem 2
x + 2.9 = -1.55241747 Simplifying x + 2.9 = -1.55241747 Reorder the terms: 2.9 + x = -1.55241747 Solving 2.9 + x = -1.55241747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + x = -1.55241747 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + x = -1.55241747 + -2.9 x = -1.55241747 + -2.9 Combine like terms: -1.55241747 + -2.9 = -4.45241747 x = -4.45241747 Simplifying x = -4.45241747Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.34758253, -4.45241747}
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