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Simplifying 40x2 + 1200x + -60 = 0 Reorder the terms: -60 + 1200x + 40x2 = 0 Solving -60 + 1200x + 40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20'. 20(-3 + 60x + 2x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-3 + 60x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + 60x + 2x2 = 0 Solving -3 + 60x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 30x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 30x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 30x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 30x + x2 = 0 + 1.5 30x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 30x + x2 = 1.5 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 1.5 + 225 Reorder the terms: 225 + 30x + x2 = 1.5 + 225 Combine like terms: 1.5 + 225 = 226.5 225 + 30x + x2 = 226.5 Factor a perfect square on the left side: (x + 15)(x + 15) = 226.5 Calculate the square root of the right side: 15.049916943 Break this problem into two subproblems by setting (x + 15) equal to 15.049916943 and -15.049916943.Subproblem 1
x + 15 = 15.049916943 Simplifying x + 15 = 15.049916943 Reorder the terms: 15 + x = 15.049916943 Solving 15 + x = 15.049916943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 15.049916943 + -15 Combine like terms: 15 + -15 = 0 0 + x = 15.049916943 + -15 x = 15.049916943 + -15 Combine like terms: 15.049916943 + -15 = 0.049916943 x = 0.049916943 Simplifying x = 0.049916943Subproblem 2
x + 15 = -15.049916943 Simplifying x + 15 = -15.049916943 Reorder the terms: 15 + x = -15.049916943 Solving 15 + x = -15.049916943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -15.049916943 + -15 Combine like terms: 15 + -15 = 0 0 + x = -15.049916943 + -15 x = -15.049916943 + -15 Combine like terms: -15.049916943 + -15 = -30.049916943 x = -30.049916943 Simplifying x = -30.049916943Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.049916943, -30.049916943}Solution
x = {0.049916943, -30.049916943}
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