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Simplifying 0 = 36x2 + -360x + -150 Reorder the terms: 0 = -150 + -360x + 36x2 Solving 0 = -150 + -360x + 36x2 Solving for variable 'x'. Combine like terms: 0 + 150 = 150 150 + 360x + -36x2 = -150 + -360x + 36x2 + 150 + 360x + -36x2 Reorder the terms: 150 + 360x + -36x2 = -150 + 150 + -360x + 360x + 36x2 + -36x2 Combine like terms: -150 + 150 = 0 150 + 360x + -36x2 = 0 + -360x + 360x + 36x2 + -36x2 150 + 360x + -36x2 = -360x + 360x + 36x2 + -36x2 Combine like terms: -360x + 360x = 0 150 + 360x + -36x2 = 0 + 36x2 + -36x2 150 + 360x + -36x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 150 + 360x + -36x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(25 + 60x + -6x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(25 + 60x + -6x2)' equal to zero and attempt to solve: Simplifying 25 + 60x + -6x2 = 0 Solving 25 + 60x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -4.166666667 + -10x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + -10x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + -10x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + -10x + x2 = 0 + 4.166666667 -10x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 -10x + x2 = 4.166666667 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 = 4.166666667 + 25 Reorder the terms: 25 + -10x + x2 = 4.166666667 + 25 Combine like terms: 4.166666667 + 25 = 29.166666667 25 + -10x + x2 = 29.166666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 29.166666667 Calculate the square root of the right side: 5.400617249 Break this problem into two subproblems by setting (x + -5) equal to 5.400617249 and -5.400617249.Subproblem 1
x + -5 = 5.400617249 Simplifying x + -5 = 5.400617249 Reorder the terms: -5 + x = 5.400617249 Solving -5 + x = 5.400617249 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 = 5.400617249 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.400617249 + 5 x = 5.400617249 + 5 Combine like terms: 5.400617249 + 5 = 10.400617249 x = 10.400617249 Simplifying x = 10.400617249Subproblem 2
x + -5 = -5.400617249 Simplifying x + -5 = -5.400617249 Reorder the terms: -5 + x = -5.400617249 Solving -5 + x = -5.400617249 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 = -5.400617249 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.400617249 + 5 x = -5.400617249 + 5 Combine like terms: -5.400617249 + 5 = -0.400617249 x = -0.400617249 Simplifying x = -0.400617249Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.400617249, -0.400617249}Solution
x = {10.400617249, -0.400617249}
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