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Simplifying 3x(2x + 7) = 2(3x + 11) Reorder the terms: 3x(7 + 2x) = 2(3x + 11) (7 * 3x + 2x * 3x) = 2(3x + 11) (21x + 6x2) = 2(3x + 11) Reorder the terms: 21x + 6x2 = 2(11 + 3x) 21x + 6x2 = (11 * 2 + 3x * 2) 21x + 6x2 = (22 + 6x) Solving 21x + 6x2 = 22 + 6x Solving for variable 'x'. Reorder the terms: -22 + 21x + -6x + 6x2 = 22 + 6x + -22 + -6x Combine like terms: 21x + -6x = 15x -22 + 15x + 6x2 = 22 + 6x + -22 + -6x Reorder the terms: -22 + 15x + 6x2 = 22 + -22 + 6x + -6x Combine like terms: 22 + -22 = 0 -22 + 15x + 6x2 = 0 + 6x + -6x -22 + 15x + 6x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -22 + 15x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.666666667 + 2.5x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 2.5x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 2.5x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 2.5x + x2 = 0 + 3.666666667 2.5x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 2.5x + x2 = 3.666666667 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 3.666666667 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 3.666666667 + 1.5625 Combine like terms: 3.666666667 + 1.5625 = 5.229166667 1.5625 + 2.5x + x2 = 5.229166667 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 5.229166667 Calculate the square root of the right side: 2.286737122 Break this problem into two subproblems by setting (x + 1.25) equal to 2.286737122 and -2.286737122.Subproblem 1
x + 1.25 = 2.286737122 Simplifying x + 1.25 = 2.286737122 Reorder the terms: 1.25 + x = 2.286737122 Solving 1.25 + x = 2.286737122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.286737122 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.286737122 + -1.25 x = 2.286737122 + -1.25 Combine like terms: 2.286737122 + -1.25 = 1.036737122 x = 1.036737122 Simplifying x = 1.036737122Subproblem 2
x + 1.25 = -2.286737122 Simplifying x + 1.25 = -2.286737122 Reorder the terms: 1.25 + x = -2.286737122 Solving 1.25 + x = -2.286737122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.286737122 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.286737122 + -1.25 x = -2.286737122 + -1.25 Combine like terms: -2.286737122 + -1.25 = -3.536737122 x = -3.536737122 Simplifying x = -3.536737122Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.036737122, -3.536737122}
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