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Simplifying (2x + 3)(x + -7) = 25 Reorder the terms: (3 + 2x)(x + -7) = 25 Reorder the terms: (3 + 2x)(-7 + x) = 25 Multiply (3 + 2x) * (-7 + x) (3(-7 + x) + 2x * (-7 + x)) = 25 ((-7 * 3 + x * 3) + 2x * (-7 + x)) = 25 ((-21 + 3x) + 2x * (-7 + x)) = 25 (-21 + 3x + (-7 * 2x + x * 2x)) = 25 (-21 + 3x + (-14x + 2x2)) = 25 Combine like terms: 3x + -14x = -11x (-21 + -11x + 2x2) = 25 Solving -21 + -11x + 2x2 = 25 Solving for variable 'x'. Reorder the terms: -21 + -25 + -11x + 2x2 = 25 + -25 Combine like terms: -21 + -25 = -46 -46 + -11x + 2x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -46 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23 + -5.5x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + -5.5x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -5.5x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -5.5x + x2 = 0 + 23 -5.5x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -5.5x + x2 = 23 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 23 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 23 + 7.5625 Combine like terms: 23 + 7.5625 = 30.5625 7.5625 + -5.5x + x2 = 30.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 30.5625 Calculate the square root of the right side: 5.528336097 Break this problem into two subproblems by setting (x + -2.75) equal to 5.528336097 and -5.528336097.Subproblem 1
x + -2.75 = 5.528336097 Simplifying x + -2.75 = 5.528336097 Reorder the terms: -2.75 + x = 5.528336097 Solving -2.75 + x = 5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 5.528336097 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 5.528336097 + 2.75 x = 5.528336097 + 2.75 Combine like terms: 5.528336097 + 2.75 = 8.278336097 x = 8.278336097 Simplifying x = 8.278336097Subproblem 2
x + -2.75 = -5.528336097 Simplifying x + -2.75 = -5.528336097 Reorder the terms: -2.75 + x = -5.528336097 Solving -2.75 + x = -5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -5.528336097 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -5.528336097 + 2.75 x = -5.528336097 + 2.75 Combine like terms: -5.528336097 + 2.75 = -2.778336097 x = -2.778336097 Simplifying x = -2.778336097Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.278336097, -2.778336097}
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