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Simplifying (5x + 12) * 3x = 8 Reorder the terms: (12 + 5x) * 3x = 8 Reorder the terms for easier multiplication: 3x(12 + 5x) = 8 (12 * 3x + 5x * 3x) = 8 (36x + 15x2) = 8 Solving 36x + 15x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 36x + 15x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 36x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.5333333333 + 2.4x + x2 = 0 Move the constant term to the right: Add '0.5333333333' to each side of the equation. -0.5333333333 + 2.4x + 0.5333333333 + x2 = 0 + 0.5333333333 Reorder the terms: -0.5333333333 + 0.5333333333 + 2.4x + x2 = 0 + 0.5333333333 Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000 0.0000000000 + 2.4x + x2 = 0 + 0.5333333333 2.4x + x2 = 0 + 0.5333333333 Combine like terms: 0 + 0.5333333333 = 0.5333333333 2.4x + x2 = 0.5333333333 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 0.5333333333 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 0.5333333333 + 1.44 Combine like terms: 0.5333333333 + 1.44 = 1.9733333333 1.44 + 2.4x + x2 = 1.9733333333 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 1.9733333333 Calculate the square root of the right side: 1.404753834 Break this problem into two subproblems by setting (x + 1.2) equal to 1.404753834 and -1.404753834.Subproblem 1
x + 1.2 = 1.404753834 Simplifying x + 1.2 = 1.404753834 Reorder the terms: 1.2 + x = 1.404753834 Solving 1.2 + x = 1.404753834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.404753834 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.404753834 + -1.2 x = 1.404753834 + -1.2 Combine like terms: 1.404753834 + -1.2 = 0.204753834 x = 0.204753834 Simplifying x = 0.204753834Subproblem 2
x + 1.2 = -1.404753834 Simplifying x + 1.2 = -1.404753834 Reorder the terms: 1.2 + x = -1.404753834 Solving 1.2 + x = -1.404753834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.404753834 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.404753834 + -1.2 x = -1.404753834 + -1.2 Combine like terms: -1.404753834 + -1.2 = -2.604753834 x = -2.604753834 Simplifying x = -2.604753834Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.204753834, -2.604753834}
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