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Simplifying 3 = (x + -7)(x + 5) Reorder the terms: 3 = (-7 + x)(x + 5) Reorder the terms: 3 = (-7 + x)(5 + x) Multiply (-7 + x) * (5 + x) 3 = (-7(5 + x) + x(5 + x)) 3 = ((5 * -7 + x * -7) + x(5 + x)) 3 = ((-35 + -7x) + x(5 + x)) 3 = (-35 + -7x + (5 * x + x * x)) 3 = (-35 + -7x + (5x + x2)) Combine like terms: -7x + 5x = -2x 3 = (-35 + -2x + x2) Solving 3 = -35 + -2x + x2 Solving for variable 'x'. Combine like terms: 3 + 35 = 38 38 + 2x + -1x2 = -35 + -2x + x2 + 35 + 2x + -1x2 Reorder the terms: 38 + 2x + -1x2 = -35 + 35 + -2x + 2x + x2 + -1x2 Combine like terms: -35 + 35 = 0 38 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2 38 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 38 + 2x + -1x2 = 0 + x2 + -1x2 38 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 38 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -38 + -2x + x2 = 0 Move the constant term to the right: Add '38' to each side of the equation. -38 + -2x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -2x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -2x + x2 = 0 + 38 -2x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -2x + x2 = 38 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 38 + 1 Reorder the terms: 1 + -2x + x2 = 38 + 1 Combine like terms: 38 + 1 = 39 1 + -2x + x2 = 39 Factor a perfect square on the left side: (x + -1)(x + -1) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + -1) equal to 6.244997998 and -6.244997998.Subproblem 1
x + -1 = 6.244997998 Simplifying x + -1 = 6.244997998 Reorder the terms: -1 + x = 6.244997998 Solving -1 + x = 6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 6.244997998 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.244997998 + 1 x = 6.244997998 + 1 Combine like terms: 6.244997998 + 1 = 7.244997998 x = 7.244997998 Simplifying x = 7.244997998Subproblem 2
x + -1 = -6.244997998 Simplifying x + -1 = -6.244997998 Reorder the terms: -1 + x = -6.244997998 Solving -1 + x = -6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -6.244997998 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.244997998 + 1 x = -6.244997998 + 1 Combine like terms: -6.244997998 + 1 = -5.244997998 x = -5.244997998 Simplifying x = -5.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.244997998, -5.244997998}
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