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Simplifying 5x(x + 2) + 6 = 3 Reorder the terms: 5x(2 + x) + 6 = 3 (2 * 5x + x * 5x) + 6 = 3 (10x + 5x2) + 6 = 3 Reorder the terms: 6 + 10x + 5x2 = 3 Solving 6 + 10x + 5x2 = 3 Solving for variable 'x'. Reorder the terms: 6 + -3 + 10x + 5x2 = 3 + -3 Combine like terms: 6 + -3 = 3 3 + 10x + 5x2 = 3 + -3 Combine like terms: 3 + -3 = 0 3 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 2x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 2x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 2x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 2x + x2 = 0 + -0.6 2x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 2x + x2 = -0.6 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.6 + 1 Reorder the terms: 1 + 2x + x2 = -0.6 + 1 Combine like terms: -0.6 + 1 = 0.4 1 + 2x + x2 = 0.4 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.4 Calculate the square root of the right side: 0.632455532 Break this problem into two subproblems by setting (x + 1) equal to 0.632455532 and -0.632455532.Subproblem 1
x + 1 = 0.632455532 Simplifying x + 1 = 0.632455532 Reorder the terms: 1 + x = 0.632455532 Solving 1 + x = 0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.632455532 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.632455532 + -1 x = 0.632455532 + -1 Combine like terms: 0.632455532 + -1 = -0.367544468 x = -0.367544468 Simplifying x = -0.367544468Subproblem 2
x + 1 = -0.632455532 Simplifying x + 1 = -0.632455532 Reorder the terms: 1 + x = -0.632455532 Solving 1 + x = -0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.632455532 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.632455532 + -1 x = -0.632455532 + -1 Combine like terms: -0.632455532 + -1 = -1.632455532 x = -1.632455532 Simplifying x = -1.632455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.367544468, -1.632455532}
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