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Simplifying 924 = 3x2 + 30x + 60 Reorder the terms: 924 = 60 + 30x + 3x2 Solving 924 = 60 + 30x + 3x2 Solving for variable 'x'. Combine like terms: 924 + -60 = 864 864 + -30x + -3x2 = 60 + 30x + 3x2 + -60 + -30x + -3x2 Reorder the terms: 864 + -30x + -3x2 = 60 + -60 + 30x + -30x + 3x2 + -3x2 Combine like terms: 60 + -60 = 0 864 + -30x + -3x2 = 0 + 30x + -30x + 3x2 + -3x2 864 + -30x + -3x2 = 30x + -30x + 3x2 + -3x2 Combine like terms: 30x + -30x = 0 864 + -30x + -3x2 = 0 + 3x2 + -3x2 864 + -30x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 864 + -30x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(288 + -10x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(288 + -10x + -1x2)' equal to zero and attempt to solve: Simplifying 288 + -10x + -1x2 = 0 Solving 288 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -288 + 10x + x2 = 0 Move the constant term to the right: Add '288' to each side of the equation. -288 + 10x + 288 + x2 = 0 + 288 Reorder the terms: -288 + 288 + 10x + x2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 10x + x2 = 0 + 288 10x + x2 = 0 + 288 Combine like terms: 0 + 288 = 288 10x + x2 = 288 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 288 + 25 Reorder the terms: 25 + 10x + x2 = 288 + 25 Combine like terms: 288 + 25 = 313 25 + 10x + x2 = 313 Factor a perfect square on the left side: (x + 5)(x + 5) = 313 Calculate the square root of the right side: 17.691806013 Break this problem into two subproblems by setting (x + 5) equal to 17.691806013 and -17.691806013.Subproblem 1
x + 5 = 17.691806013 Simplifying x + 5 = 17.691806013 Reorder the terms: 5 + x = 17.691806013 Solving 5 + x = 17.691806013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 17.691806013 + -5 Combine like terms: 5 + -5 = 0 0 + x = 17.691806013 + -5 x = 17.691806013 + -5 Combine like terms: 17.691806013 + -5 = 12.691806013 x = 12.691806013 Simplifying x = 12.691806013Subproblem 2
x + 5 = -17.691806013 Simplifying x + 5 = -17.691806013 Reorder the terms: 5 + x = -17.691806013 Solving 5 + x = -17.691806013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -17.691806013 + -5 Combine like terms: 5 + -5 = 0 0 + x = -17.691806013 + -5 x = -17.691806013 + -5 Combine like terms: -17.691806013 + -5 = -22.691806013 x = -22.691806013 Simplifying x = -22.691806013Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.691806013, -22.691806013}Solution
x = {12.691806013, -22.691806013}
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