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Simplifying 3x(x + 7) = 32 Reorder the terms: 3x(7 + x) = 32 (7 * 3x + x * 3x) = 32 (21x + 3x2) = 32 Solving 21x + 3x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 21x + 3x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 21x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.66666667 + 7x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + 7x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + 7x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + 7x + x2 = 0 + 10.66666667 7x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 7x + x2 = 10.66666667 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 10.66666667 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 10.66666667 + 12.25 Combine like terms: 10.66666667 + 12.25 = 22.91666667 12.25 + 7x + x2 = 22.91666667 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 22.91666667 Calculate the square root of the right side: 4.787135539 Break this problem into two subproblems by setting (x + 3.5) equal to 4.787135539 and -4.787135539.Subproblem 1
x + 3.5 = 4.787135539 Simplifying x + 3.5 = 4.787135539 Reorder the terms: 3.5 + x = 4.787135539 Solving 3.5 + x = 4.787135539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.787135539 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.787135539 + -3.5 x = 4.787135539 + -3.5 Combine like terms: 4.787135539 + -3.5 = 1.287135539 x = 1.287135539 Simplifying x = 1.287135539Subproblem 2
x + 3.5 = -4.787135539 Simplifying x + 3.5 = -4.787135539 Reorder the terms: 3.5 + x = -4.787135539 Solving 3.5 + x = -4.787135539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.787135539 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.787135539 + -3.5 x = -4.787135539 + -3.5 Combine like terms: -4.787135539 + -3.5 = -8.287135539 x = -8.287135539 Simplifying x = -8.287135539Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.287135539, -8.287135539}
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