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Simplifying 3x * x + -30x = 360 Multiply x * x 3x2 + -30x = 360 Reorder the terms: -30x + 3x2 = 360 Solving -30x + 3x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + -30x + 3x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + -30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-120 + -10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-120 + -10x + x2)' equal to zero and attempt to solve: Simplifying -120 + -10x + x2 = 0 Solving -120 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + -10x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -10x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -10x + x2 = 0 + 120 -10x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -10x + x2 = 120 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 = 120 + 25 Reorder the terms: 25 + -10x + x2 = 120 + 25 Combine like terms: 120 + 25 = 145 25 + -10x + x2 = 145 Factor a perfect square on the left side: (x + -5)(x + -5) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + -5) equal to 12.041594579 and -12.041594579.Subproblem 1
x + -5 = 12.041594579 Simplifying x + -5 = 12.041594579 Reorder the terms: -5 + x = 12.041594579 Solving -5 + x = 12.041594579 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 = 12.041594579 + 5 Combine like terms: -5 + 5 = 0 0 + x = 12.041594579 + 5 x = 12.041594579 + 5 Combine like terms: 12.041594579 + 5 = 17.041594579 x = 17.041594579 Simplifying x = 17.041594579Subproblem 2
x + -5 = -12.041594579 Simplifying x + -5 = -12.041594579 Reorder the terms: -5 + x = -12.041594579 Solving -5 + x = -12.041594579 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 = -12.041594579 + 5 Combine like terms: -5 + 5 = 0 0 + x = -12.041594579 + 5 x = -12.041594579 + 5 Combine like terms: -12.041594579 + 5 = -7.041594579 x = -7.041594579 Simplifying x = -7.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.041594579, -7.041594579}Solution
x = {17.041594579, -7.041594579}
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