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Simplifying 3x(x + 3) = 92 Reorder the terms: 3x(3 + x) = 92 (3 * 3x + x * 3x) = 92 (9x + 3x2) = 92 Solving 9x + 3x2 = 92 Solving for variable 'x'. Reorder the terms: -92 + 9x + 3x2 = 92 + -92 Combine like terms: 92 + -92 = 0 -92 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30.66666667 + 3x + x2 = 0 Move the constant term to the right: Add '30.66666667' to each side of the equation. -30.66666667 + 3x + 30.66666667 + x2 = 0 + 30.66666667 Reorder the terms: -30.66666667 + 30.66666667 + 3x + x2 = 0 + 30.66666667 Combine like terms: -30.66666667 + 30.66666667 = 0.00000000 0.00000000 + 3x + x2 = 0 + 30.66666667 3x + x2 = 0 + 30.66666667 Combine like terms: 0 + 30.66666667 = 30.66666667 3x + x2 = 30.66666667 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 30.66666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 30.66666667 + 2.25 Combine like terms: 30.66666667 + 2.25 = 32.91666667 2.25 + 3x + x2 = 32.91666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 32.91666667 Calculate the square root of the right side: 5.737304826 Break this problem into two subproblems by setting (x + 1.5) equal to 5.737304826 and -5.737304826.Subproblem 1
x + 1.5 = 5.737304826 Simplifying x + 1.5 = 5.737304826 Reorder the terms: 1.5 + x = 5.737304826 Solving 1.5 + x = 5.737304826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 5.737304826 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.737304826 + -1.5 x = 5.737304826 + -1.5 Combine like terms: 5.737304826 + -1.5 = 4.237304826 x = 4.237304826 Simplifying x = 4.237304826Subproblem 2
x + 1.5 = -5.737304826 Simplifying x + 1.5 = -5.737304826 Reorder the terms: 1.5 + x = -5.737304826 Solving 1.5 + x = -5.737304826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -5.737304826 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.737304826 + -1.5 x = -5.737304826 + -1.5 Combine like terms: -5.737304826 + -1.5 = -7.237304826 x = -7.237304826 Simplifying x = -7.237304826Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.237304826, -7.237304826}
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