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Simplifying 5x2 + 60x + 90 = 0 Reorder the terms: 90 + 60x + 5x2 = 0 Solving 90 + 60x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(18 + 12x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(18 + 12x + x2)' equal to zero and attempt to solve: Simplifying 18 + 12x + x2 = 0 Solving 18 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 12x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 12x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 12x + x2 = 0 + -18 12x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 12x + x2 = -18 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 = -18 + 36 Reorder the terms: 36 + 12x + x2 = -18 + 36 Combine like terms: -18 + 36 = 18 36 + 12x + x2 = 18 Factor a perfect square on the left side: (x + 6)(x + 6) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 6) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 6 = 4.242640687 Simplifying x + 6 = 4.242640687 Reorder the terms: 6 + x = 4.242640687 Solving 6 + x = 4.242640687 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 = 4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.242640687 + -6 x = 4.242640687 + -6 Combine like terms: 4.242640687 + -6 = -1.757359313 x = -1.757359313 Simplifying x = -1.757359313Subproblem 2
x + 6 = -4.242640687 Simplifying x + 6 = -4.242640687 Reorder the terms: 6 + x = -4.242640687 Solving 6 + x = -4.242640687 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 = -4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.242640687 + -6 x = -4.242640687 + -6 Combine like terms: -4.242640687 + -6 = -10.242640687 x = -10.242640687 Simplifying x = -10.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.757359313, -10.242640687}Solution
x = {-1.757359313, -10.242640687}
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