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Simplifying x2 = (2x + -7)(2x + 13) Reorder the terms: x2 = (-7 + 2x)(2x + 13) Reorder the terms: x2 = (-7 + 2x)(13 + 2x) Multiply (-7 + 2x) * (13 + 2x) x2 = (-7(13 + 2x) + 2x * (13 + 2x)) x2 = ((13 * -7 + 2x * -7) + 2x * (13 + 2x)) x2 = ((-91 + -14x) + 2x * (13 + 2x)) x2 = (-91 + -14x + (13 * 2x + 2x * 2x)) x2 = (-91 + -14x + (26x + 4x2)) Combine like terms: -14x + 26x = 12x x2 = (-91 + 12x + 4x2) Solving x2 = -91 + 12x + 4x2 Solving for variable 'x'. Reorder the terms: 91 + -12x + x2 + -4x2 = -91 + 12x + 4x2 + 91 + -12x + -4x2 Combine like terms: x2 + -4x2 = -3x2 91 + -12x + -3x2 = -91 + 12x + 4x2 + 91 + -12x + -4x2 Reorder the terms: 91 + -12x + -3x2 = -91 + 91 + 12x + -12x + 4x2 + -4x2 Combine like terms: -91 + 91 = 0 91 + -12x + -3x2 = 0 + 12x + -12x + 4x2 + -4x2 91 + -12x + -3x2 = 12x + -12x + 4x2 + -4x2 Combine like terms: 12x + -12x = 0 91 + -12x + -3x2 = 0 + 4x2 + -4x2 91 + -12x + -3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 91 + -12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -30.33333333 + 4x + x2 = 0 Move the constant term to the right: Add '30.33333333' to each side of the equation. -30.33333333 + 4x + 30.33333333 + x2 = 0 + 30.33333333 Reorder the terms: -30.33333333 + 30.33333333 + 4x + x2 = 0 + 30.33333333 Combine like terms: -30.33333333 + 30.33333333 = 0.00000000 0.00000000 + 4x + x2 = 0 + 30.33333333 4x + x2 = 0 + 30.33333333 Combine like terms: 0 + 30.33333333 = 30.33333333 4x + x2 = 30.33333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 30.33333333 + 4 Reorder the terms: 4 + 4x + x2 = 30.33333333 + 4 Combine like terms: 30.33333333 + 4 = 34.33333333 4 + 4x + x2 = 34.33333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 34.33333333 Calculate the square root of the right side: 5.859465277 Break this problem into two subproblems by setting (x + 2) equal to 5.859465277 and -5.859465277.Subproblem 1
x + 2 = 5.859465277 Simplifying x + 2 = 5.859465277 Reorder the terms: 2 + x = 5.859465277 Solving 2 + x = 5.859465277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.859465277 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.859465277 + -2 x = 5.859465277 + -2 Combine like terms: 5.859465277 + -2 = 3.859465277 x = 3.859465277 Simplifying x = 3.859465277Subproblem 2
x + 2 = -5.859465277 Simplifying x + 2 = -5.859465277 Reorder the terms: 2 + x = -5.859465277 Solving 2 + x = -5.859465277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.859465277 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.859465277 + -2 x = -5.859465277 + -2 Combine like terms: -5.859465277 + -2 = -7.859465277 x = -7.859465277 Simplifying x = -7.859465277Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.859465277, -7.859465277}
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