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Simplifying (x + 3)(2x + 1) = 15 Reorder the terms: (3 + x)(2x + 1) = 15 Reorder the terms: (3 + x)(1 + 2x) = 15 Multiply (3 + x) * (1 + 2x) (3(1 + 2x) + x(1 + 2x)) = 15 ((1 * 3 + 2x * 3) + x(1 + 2x)) = 15 ((3 + 6x) + x(1 + 2x)) = 15 (3 + 6x + (1 * x + 2x * x)) = 15 (3 + 6x + (1x + 2x2)) = 15 Combine like terms: 6x + 1x = 7x (3 + 7x + 2x2) = 15 Solving 3 + 7x + 2x2 = 15 Solving for variable 'x'. Reorder the terms: 3 + -15 + 7x + 2x2 = 15 + -15 Combine like terms: 3 + -15 = -12 -12 + 7x + 2x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -12 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + 3.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 3.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 3.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3.5x + x2 = 0 + 6 3.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 3.5x + x2 = 6 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 6 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 6 + 3.0625 Combine like terms: 6 + 3.0625 = 9.0625 3.0625 + 3.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + 1.75) equal to 3.010398645 and -3.010398645.Subproblem 1
x + 1.75 = 3.010398645 Simplifying x + 1.75 = 3.010398645 Reorder the terms: 1.75 + x = 3.010398645 Solving 1.75 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.010398645 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.010398645 + -1.75 x = 3.010398645 + -1.75 Combine like terms: 3.010398645 + -1.75 = 1.260398645 x = 1.260398645 Simplifying x = 1.260398645Subproblem 2
x + 1.75 = -3.010398645 Simplifying x + 1.75 = -3.010398645 Reorder the terms: 1.75 + x = -3.010398645 Solving 1.75 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.010398645 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.010398645 + -1.75 x = -3.010398645 + -1.75 Combine like terms: -3.010398645 + -1.75 = -4.760398645 x = -4.760398645 Simplifying x = -4.760398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.260398645, -4.760398645}
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