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Simplifying 5x2 + 60x + -900 = 0 Reorder the terms: -900 + 60x + 5x2 = 0 Solving -900 + 60x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-180 + 12x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-180 + 12x + x2)' equal to zero and attempt to solve: Simplifying -180 + 12x + x2 = 0 Solving -180 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 12x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 12x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 12x + x2 = 0 + 180 12x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 12x + x2 = 180 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 180 + 36 Reorder the terms: 36 + 12x + x2 = 180 + 36 Combine like terms: 180 + 36 = 216 36 + 12x + x2 = 216 Factor a perfect square on the left side: (x + 6)(x + 6) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (x + 6) equal to 14.696938457 and -14.696938457.Subproblem 1
x + 6 = 14.696938457 Simplifying x + 6 = 14.696938457 Reorder the terms: 6 + x = 14.696938457 Solving 6 + x = 14.696938457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 14.696938457 + -6 Combine like terms: 6 + -6 = 0 0 + x = 14.696938457 + -6 x = 14.696938457 + -6 Combine like terms: 14.696938457 + -6 = 8.696938457 x = 8.696938457 Simplifying x = 8.696938457Subproblem 2
x + 6 = -14.696938457 Simplifying x + 6 = -14.696938457 Reorder the terms: 6 + x = -14.696938457 Solving 6 + x = -14.696938457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -14.696938457 + -6 Combine like terms: 6 + -6 = 0 0 + x = -14.696938457 + -6 x = -14.696938457 + -6 Combine like terms: -14.696938457 + -6 = -20.696938457 x = -20.696938457 Simplifying x = -20.696938457Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.696938457, -20.696938457}Solution
x = {8.696938457, -20.696938457}
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