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Simplifying 3x2 + -30x = 174 Reorder the terms: -30x + 3x2 = 174 Solving -30x + 3x2 = 174 Solving for variable 'x'. Reorder the terms: -174 + -30x + 3x2 = 174 + -174 Combine like terms: 174 + -174 = 0 -174 + -30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-58 + -10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-58 + -10x + x2)' equal to zero and attempt to solve: Simplifying -58 + -10x + x2 = 0 Solving -58 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + -10x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + -10x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -10x + x2 = 0 + 58 -10x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 -10x + x2 = 58 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 = 58 + 25 Reorder the terms: 25 + -10x + x2 = 58 + 25 Combine like terms: 58 + 25 = 83 25 + -10x + x2 = 83 Factor a perfect square on the left side: (x + -5)(x + -5) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (x + -5) equal to 9.110433579 and -9.110433579.Subproblem 1
x + -5 = 9.110433579 Simplifying x + -5 = 9.110433579 Reorder the terms: -5 + x = 9.110433579 Solving -5 + x = 9.110433579 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 = 9.110433579 + 5 Combine like terms: -5 + 5 = 0 0 + x = 9.110433579 + 5 x = 9.110433579 + 5 Combine like terms: 9.110433579 + 5 = 14.110433579 x = 14.110433579 Simplifying x = 14.110433579Subproblem 2
x + -5 = -9.110433579 Simplifying x + -5 = -9.110433579 Reorder the terms: -5 + x = -9.110433579 Solving -5 + x = -9.110433579 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 = -9.110433579 + 5 Combine like terms: -5 + 5 = 0 0 + x = -9.110433579 + 5 x = -9.110433579 + 5 Combine like terms: -9.110433579 + 5 = -4.110433579 x = -4.110433579 Simplifying x = -4.110433579Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.110433579, -4.110433579}Solution
x = {14.110433579, -4.110433579}
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