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Simplifying 3x2 + 18x = 2280 Reorder the terms: 18x + 3x2 = 2280 Solving 18x + 3x2 = 2280 Solving for variable 'x'. Reorder the terms: -2280 + 18x + 3x2 = 2280 + -2280 Combine like terms: 2280 + -2280 = 0 -2280 + 18x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-760 + 6x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-760 + 6x + x2)' equal to zero and attempt to solve: Simplifying -760 + 6x + x2 = 0 Solving -760 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '760' to each side of the equation. -760 + 6x + 760 + x2 = 0 + 760 Reorder the terms: -760 + 760 + 6x + x2 = 0 + 760 Combine like terms: -760 + 760 = 0 0 + 6x + x2 = 0 + 760 6x + x2 = 0 + 760 Combine like terms: 0 + 760 = 760 6x + x2 = 760 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 760 + 9 Reorder the terms: 9 + 6x + x2 = 760 + 9 Combine like terms: 760 + 9 = 769 9 + 6x + x2 = 769 Factor a perfect square on the left side: (x + 3)(x + 3) = 769 Calculate the square root of the right side: 27.730849248 Break this problem into two subproblems by setting (x + 3) equal to 27.730849248 and -27.730849248.Subproblem 1
x + 3 = 27.730849248 Simplifying x + 3 = 27.730849248 Reorder the terms: 3 + x = 27.730849248 Solving 3 + x = 27.730849248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 27.730849248 + -3 Combine like terms: 3 + -3 = 0 0 + x = 27.730849248 + -3 x = 27.730849248 + -3 Combine like terms: 27.730849248 + -3 = 24.730849248 x = 24.730849248 Simplifying x = 24.730849248Subproblem 2
x + 3 = -27.730849248 Simplifying x + 3 = -27.730849248 Reorder the terms: 3 + x = -27.730849248 Solving 3 + x = -27.730849248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -27.730849248 + -3 Combine like terms: 3 + -3 = 0 0 + x = -27.730849248 + -3 x = -27.730849248 + -3 Combine like terms: -27.730849248 + -3 = -30.730849248 x = -30.730849248 Simplifying x = -30.730849248Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.730849248, -30.730849248}Solution
x = {24.730849248, -30.730849248}
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