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Simplifying 10x2 + 60x + 36 = 0 Reorder the terms: 36 + 60x + 10x2 = 0 Solving 36 + 60x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + 30x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + 30x + 5x2)' equal to zero and attempt to solve: Simplifying 18 + 30x + 5x2 = 0 Solving 18 + 30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.6 + 6x + x2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + 6x + -3.6 + x2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + 6x + x2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + 6x + x2 = 0 + -3.6 6x + x2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 6x + x2 = -3.6 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -3.6 + 9 Reorder the terms: 9 + 6x + x2 = -3.6 + 9 Combine like terms: -3.6 + 9 = 5.4 9 + 6x + x2 = 5.4 Factor a perfect square on the left side: (x + 3)(x + 3) = 5.4 Calculate the square root of the right side: 2.323790008 Break this problem into two subproblems by setting (x + 3) equal to 2.323790008 and -2.323790008.Subproblem 1
x + 3 = 2.323790008 Simplifying x + 3 = 2.323790008 Reorder the terms: 3 + x = 2.323790008 Solving 3 + x = 2.323790008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.323790008 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.323790008 + -3 x = 2.323790008 + -3 Combine like terms: 2.323790008 + -3 = -0.676209992 x = -0.676209992 Simplifying x = -0.676209992Subproblem 2
x + 3 = -2.323790008 Simplifying x + 3 = -2.323790008 Reorder the terms: 3 + x = -2.323790008 Solving 3 + x = -2.323790008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.323790008 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.323790008 + -3 x = -2.323790008 + -3 Combine like terms: -2.323790008 + -3 = -5.323790008 x = -5.323790008 Simplifying x = -5.323790008Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.676209992, -5.323790008}Solution
x = {-0.676209992, -5.323790008}
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