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Simplifying (x + -3)(2x + 1) = 7 Reorder the terms: (-3 + x)(2x + 1) = 7 Reorder the terms: (-3 + x)(1 + 2x) = 7 Multiply (-3 + x) * (1 + 2x) (-3(1 + 2x) + x(1 + 2x)) = 7 ((1 * -3 + 2x * -3) + x(1 + 2x)) = 7 ((-3 + -6x) + x(1 + 2x)) = 7 (-3 + -6x + (1 * x + 2x * x)) = 7 (-3 + -6x + (1x + 2x2)) = 7 Combine like terms: -6x + 1x = -5x (-3 + -5x + 2x2) = 7 Solving -3 + -5x + 2x2 = 7 Solving for variable 'x'. Reorder the terms: -3 + -7 + -5x + 2x2 = 7 + -7 Combine like terms: -3 + -7 = -10 -10 + -5x + 2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -10 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + -2.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -2.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2.5x + x2 = 0 + 5 -2.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2.5x + x2 = 5 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 = 5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 5 + 1.5625 Combine like terms: 5 + 1.5625 = 6.5625 1.5625 + -2.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + -1.25) equal to 2.561737691 and -2.561737691.Subproblem 1
x + -1.25 = 2.561737691 Simplifying x + -1.25 = 2.561737691 Reorder the terms: -1.25 + x = 2.561737691 Solving -1.25 + x = 2.561737691 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 = 2.561737691 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.561737691 + 1.25 x = 2.561737691 + 1.25 Combine like terms: 2.561737691 + 1.25 = 3.811737691 x = 3.811737691 Simplifying x = 3.811737691Subproblem 2
x + -1.25 = -2.561737691 Simplifying x + -1.25 = -2.561737691 Reorder the terms: -1.25 + x = -2.561737691 Solving -1.25 + x = -2.561737691 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 = -2.561737691 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.561737691 + 1.25 x = -2.561737691 + 1.25 Combine like terms: -2.561737691 + 1.25 = -1.311737691 x = -1.311737691 Simplifying x = -1.311737691Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.811737691, -1.311737691}
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