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Simplifying 30 = (18 + x)(600 + -5x) Multiply (18 + x) * (600 + -5x) 30 = (18(600 + -5x) + x(600 + -5x)) 30 = ((600 * 18 + -5x * 18) + x(600 + -5x)) 30 = ((10800 + -90x) + x(600 + -5x)) 30 = (10800 + -90x + (600 * x + -5x * x)) 30 = (10800 + -90x + (600x + -5x2)) Combine like terms: -90x + 600x = 510x 30 = (10800 + 510x + -5x2) Solving 30 = 10800 + 510x + -5x2 Solving for variable 'x'. Combine like terms: 30 + -10800 = -10770 -10770 + -510x + 5x2 = 10800 + 510x + -5x2 + -10800 + -510x + 5x2 Reorder the terms: -10770 + -510x + 5x2 = 10800 + -10800 + 510x + -510x + -5x2 + 5x2 Combine like terms: 10800 + -10800 = 0 -10770 + -510x + 5x2 = 0 + 510x + -510x + -5x2 + 5x2 -10770 + -510x + 5x2 = 510x + -510x + -5x2 + 5x2 Combine like terms: 510x + -510x = 0 -10770 + -510x + 5x2 = 0 + -5x2 + 5x2 -10770 + -510x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -10770 + -510x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2154 + -102x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2154 + -102x + x2)' equal to zero and attempt to solve: Simplifying -2154 + -102x + x2 = 0 Solving -2154 + -102x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2154' to each side of the equation. -2154 + -102x + 2154 + x2 = 0 + 2154 Reorder the terms: -2154 + 2154 + -102x + x2 = 0 + 2154 Combine like terms: -2154 + 2154 = 0 0 + -102x + x2 = 0 + 2154 -102x + x2 = 0 + 2154 Combine like terms: 0 + 2154 = 2154 -102x + x2 = 2154 The x term is -102x. Take half its coefficient (-51). Square it (2601) and add it to both sides. Add '2601' to each side of the equation. -102x + 2601 + x2 = 2154 + 2601 Reorder the terms: 2601 + -102x + x2 = 2154 + 2601 Combine like terms: 2154 + 2601 = 4755 2601 + -102x + x2 = 4755 Factor a perfect square on the left side: (x + -51)(x + -51) = 4755 Calculate the square root of the right side: 68.956508032 Break this problem into two subproblems by setting (x + -51) equal to 68.956508032 and -68.956508032.Subproblem 1
x + -51 = 68.956508032 Simplifying x + -51 = 68.956508032 Reorder the terms: -51 + x = 68.956508032 Solving -51 + x = 68.956508032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + x = 68.956508032 + 51 Combine like terms: -51 + 51 = 0 0 + x = 68.956508032 + 51 x = 68.956508032 + 51 Combine like terms: 68.956508032 + 51 = 119.956508032 x = 119.956508032 Simplifying x = 119.956508032Subproblem 2
x + -51 = -68.956508032 Simplifying x + -51 = -68.956508032 Reorder the terms: -51 + x = -68.956508032 Solving -51 + x = -68.956508032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + x = -68.956508032 + 51 Combine like terms: -51 + 51 = 0 0 + x = -68.956508032 + 51 x = -68.956508032 + 51 Combine like terms: -68.956508032 + 51 = -17.956508032 x = -17.956508032 Simplifying x = -17.956508032Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.956508032, -17.956508032}Solution
x = {119.956508032, -17.956508032}
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