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Simplifying 3x + 5(2x + 6) * x = 4 Reorder the terms: 3x + 5(6 + 2x) * x = 4 Reorder the terms for easier multiplication: 3x + 5x(6 + 2x) = 4 3x + (6 * 5x + 2x * 5x) = 4 3x + (30x + 10x2) = 4 Combine like terms: 3x + 30x = 33x 33x + 10x2 = 4 Solving 33x + 10x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 33x + 10x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 33x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + 3.3x + x2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 3.3x + 0.4 + x2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + 3.3x + x2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 3.3x + x2 = 0.0 + 0.4 3.3x + x2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 3.3x + x2 = 0.4 The x term is 3.3x. Take half its coefficient (1.65). Square it (2.7225) and add it to both sides. Add '2.7225' to each side of the equation. 3.3x + 2.7225 + x2 = 0.4 + 2.7225 Reorder the terms: 2.7225 + 3.3x + x2 = 0.4 + 2.7225 Combine like terms: 0.4 + 2.7225 = 3.1225 2.7225 + 3.3x + x2 = 3.1225 Factor a perfect square on the left side: (x + 1.65)(x + 1.65) = 3.1225 Calculate the square root of the right side: 1.767059705 Break this problem into two subproblems by setting (x + 1.65) equal to 1.767059705 and -1.767059705.Subproblem 1
x + 1.65 = 1.767059705 Simplifying x + 1.65 = 1.767059705 Reorder the terms: 1.65 + x = 1.767059705 Solving 1.65 + x = 1.767059705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.65' to each side of the equation. 1.65 + -1.65 + x = 1.767059705 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + x = 1.767059705 + -1.65 x = 1.767059705 + -1.65 Combine like terms: 1.767059705 + -1.65 = 0.117059705 x = 0.117059705 Simplifying x = 0.117059705Subproblem 2
x + 1.65 = -1.767059705 Simplifying x + 1.65 = -1.767059705 Reorder the terms: 1.65 + x = -1.767059705 Solving 1.65 + x = -1.767059705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.65' to each side of the equation. 1.65 + -1.65 + x = -1.767059705 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + x = -1.767059705 + -1.65 x = -1.767059705 + -1.65 Combine like terms: -1.767059705 + -1.65 = -3.417059705 x = -3.417059705 Simplifying x = -3.417059705Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.117059705, -3.417059705}
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