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Simplifying (3x + 3)(3.4) * x = 6 Reorder the terms: (3 + 3x)(3.4) * x = 6 Reorder the terms for easier multiplication: 3.4x(3 + 3x) = 6 (3 * 3.4x + 3x * 3.4x) = 6 (10.2x + 10.2x2) = 6 Solving 10.2x + 10.2x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 10.2x + 10.2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 10.2x + 10.2x2 = 0 Begin completing the square. Divide all terms by 10.2 the coefficient of the squared term: Divide each side by '10.2'. -0.5882352941 + x + x2 = 0 Move the constant term to the right: Add '0.5882352941' to each side of the equation. -0.5882352941 + x + 0.5882352941 + x2 = 0 + 0.5882352941 Reorder the terms: -0.5882352941 + 0.5882352941 + x + x2 = 0 + 0.5882352941 Combine like terms: -0.5882352941 + 0.5882352941 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.5882352941 x + x2 = 0 + 0.5882352941 Combine like terms: 0 + 0.5882352941 = 0.5882352941 x + x2 = 0.5882352941 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.5882352941 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.5882352941 + 0.25 Combine like terms: 0.5882352941 + 0.25 = 0.8382352941 1.25 + x2 = 0.8382352941 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.8382352941 Calculate the square root of the right side: 0.915551907 Break this problem into two subproblems by setting (x + 0.5) equal to 0.915551907 and -0.915551907.Subproblem 1
x + 0.5 = 0.915551907 Simplifying x + 0.5 = 0.915551907 Reorder the terms: 0.5 + x = 0.915551907 Solving 0.5 + x = 0.915551907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.915551907 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.915551907 + -0.5 x = 0.915551907 + -0.5 Combine like terms: 0.915551907 + -0.5 = 0.415551907 x = 0.415551907 Simplifying x = 0.415551907Subproblem 2
x + 0.5 = -0.915551907 Simplifying x + 0.5 = -0.915551907 Reorder the terms: 0.5 + x = -0.915551907 Solving 0.5 + x = -0.915551907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.915551907 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.915551907 + -0.5 x = -0.915551907 + -0.5 Combine like terms: -0.915551907 + -0.5 = -1.415551907 x = -1.415551907 Simplifying x = -1.415551907Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.415551907, -1.415551907}
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