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Simplifying 240 + 68x + 4x2 = 816 Solving 240 + 68x + 4x2 = 816 Solving for variable 'x'. Reorder the terms: 240 + -816 + 68x + 4x2 = 816 + -816 Combine like terms: 240 + -816 = -576 -576 + 68x + 4x2 = 816 + -816 Combine like terms: 816 + -816 = 0 -576 + 68x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-144 + 17x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-144 + 17x + x2)' equal to zero and attempt to solve: Simplifying -144 + 17x + x2 = 0 Solving -144 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 17x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 17x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 17x + x2 = 0 + 144 17x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 17x + x2 = 144 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 144 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 144 + 72.25 Combine like terms: 144 + 72.25 = 216.25 72.25 + 17x + x2 = 216.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 216.25 Calculate the square root of the right side: 14.70544117 Break this problem into two subproblems by setting (x + 8.5) equal to 14.70544117 and -14.70544117.Subproblem 1
x + 8.5 = 14.70544117 Simplifying x + 8.5 = 14.70544117 Reorder the terms: 8.5 + x = 14.70544117 Solving 8.5 + x = 14.70544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 14.70544117 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 14.70544117 + -8.5 x = 14.70544117 + -8.5 Combine like terms: 14.70544117 + -8.5 = 6.20544117 x = 6.20544117 Simplifying x = 6.20544117Subproblem 2
x + 8.5 = -14.70544117 Simplifying x + 8.5 = -14.70544117 Reorder the terms: 8.5 + x = -14.70544117 Solving 8.5 + x = -14.70544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -14.70544117 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -14.70544117 + -8.5 x = -14.70544117 + -8.5 Combine like terms: -14.70544117 + -8.5 = -23.20544117 x = -23.20544117 Simplifying x = -23.20544117Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.20544117, -23.20544117}Solution
x = {6.20544117, -23.20544117}
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