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Simplifying (2x + -1)(x + 7) = 3x Reorder the terms: (-1 + 2x)(x + 7) = 3x Reorder the terms: (-1 + 2x)(7 + x) = 3x Multiply (-1 + 2x) * (7 + x) (-1(7 + x) + 2x * (7 + x)) = 3x ((7 * -1 + x * -1) + 2x * (7 + x)) = 3x ((-7 + -1x) + 2x * (7 + x)) = 3x (-7 + -1x + (7 * 2x + x * 2x)) = 3x (-7 + -1x + (14x + 2x2)) = 3x Combine like terms: -1x + 14x = 13x (-7 + 13x + 2x2) = 3x Solving -7 + 13x + 2x2 = 3x Solving for variable 'x'. Reorder the terms: -7 + 13x + -3x + 2x2 = 3x + -3x Combine like terms: 13x + -3x = 10x -7 + 10x + 2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -7 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 5x + x2 = 0 + 3.5 5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 5x + x2 = 3.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 3.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 3.5 + 6.25 Combine like terms: 3.5 + 6.25 = 9.75 6.25 + 5x + x2 = 9.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x + 2.5) equal to 3.122498999 and -3.122498999.Subproblem 1
x + 2.5 = 3.122498999 Simplifying x + 2.5 = 3.122498999 Reorder the terms: 2.5 + x = 3.122498999 Solving 2.5 + x = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.122498999 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.122498999 + -2.5 x = 3.122498999 + -2.5 Combine like terms: 3.122498999 + -2.5 = 0.622498999 x = 0.622498999 Simplifying x = 0.622498999Subproblem 2
x + 2.5 = -3.122498999 Simplifying x + 2.5 = -3.122498999 Reorder the terms: 2.5 + x = -3.122498999 Solving 2.5 + x = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.122498999 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.122498999 + -2.5 x = -3.122498999 + -2.5 Combine like terms: -3.122498999 + -2.5 = -5.622498999 x = -5.622498999 Simplifying x = -5.622498999Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.622498999, -5.622498999}
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