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Simplifying 265 = (x + 5)(3x + 5) Reorder the terms: 265 = (5 + x)(3x + 5) Reorder the terms: 265 = (5 + x)(5 + 3x) Multiply (5 + x) * (5 + 3x) 265 = (5(5 + 3x) + x(5 + 3x)) 265 = ((5 * 5 + 3x * 5) + x(5 + 3x)) 265 = ((25 + 15x) + x(5 + 3x)) 265 = (25 + 15x + (5 * x + 3x * x)) 265 = (25 + 15x + (5x + 3x2)) Combine like terms: 15x + 5x = 20x 265 = (25 + 20x + 3x2) Solving 265 = 25 + 20x + 3x2 Solving for variable 'x'. Combine like terms: 265 + -25 = 240 240 + -20x + -3x2 = 25 + 20x + 3x2 + -25 + -20x + -3x2 Reorder the terms: 240 + -20x + -3x2 = 25 + -25 + 20x + -20x + 3x2 + -3x2 Combine like terms: 25 + -25 = 0 240 + -20x + -3x2 = 0 + 20x + -20x + 3x2 + -3x2 240 + -20x + -3x2 = 20x + -20x + 3x2 + -3x2 Combine like terms: 20x + -20x = 0 240 + -20x + -3x2 = 0 + 3x2 + -3x2 240 + -20x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 240 + -20x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -80 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 6.666666667x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 6.666666667x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 6.666666667x + x2 = 0 + 80 6.666666667x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 6.666666667x + x2 = 80 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = 80 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 80 + 11.11111112 Combine like terms: 80 + 11.11111112 = 91.11111112 11.11111112 + 6.666666667x + x2 = 91.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 91.11111112 Calculate the square root of the right side: 9.545214043 Break this problem into two subproblems by setting (x + 3.333333334) equal to 9.545214043 and -9.545214043.Subproblem 1
x + 3.333333334 = 9.545214043 Simplifying x + 3.333333334 = 9.545214043 Reorder the terms: 3.333333334 + x = 9.545214043 Solving 3.333333334 + x = 9.545214043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 9.545214043 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 9.545214043 + -3.333333334 x = 9.545214043 + -3.333333334 Combine like terms: 9.545214043 + -3.333333334 = 6.211880709 x = 6.211880709 Simplifying x = 6.211880709Subproblem 2
x + 3.333333334 = -9.545214043 Simplifying x + 3.333333334 = -9.545214043 Reorder the terms: 3.333333334 + x = -9.545214043 Solving 3.333333334 + x = -9.545214043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -9.545214043 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -9.545214043 + -3.333333334 x = -9.545214043 + -3.333333334 Combine like terms: -9.545214043 + -3.333333334 = -12.878547377 x = -12.878547377 Simplifying x = -12.878547377Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.211880709, -12.878547377}
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