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Simplifying 4x2 + 74x + -144 = 0 Reorder the terms: -144 + 74x + 4x2 = 0 Solving -144 + 74x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + 37x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-72 + 37x + 2x2)' equal to zero and attempt to solve: Simplifying -72 + 37x + 2x2 = 0 Solving -72 + 37x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36 + 18.5x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 18.5x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 18.5x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 18.5x + x2 = 0 + 36 18.5x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 18.5x + x2 = 36 The x term is 18.5x. Take half its coefficient (9.25). Square it (85.5625) and add it to both sides. Add '85.5625' to each side of the equation. 18.5x + 85.5625 + x2 = 36 + 85.5625 Reorder the terms: 85.5625 + 18.5x + x2 = 36 + 85.5625 Combine like terms: 36 + 85.5625 = 121.5625 85.5625 + 18.5x + x2 = 121.5625 Factor a perfect square on the left side: (x + 9.25)(x + 9.25) = 121.5625 Calculate the square root of the right side: 11.025538536 Break this problem into two subproblems by setting (x + 9.25) equal to 11.025538536 and -11.025538536.Subproblem 1
x + 9.25 = 11.025538536 Simplifying x + 9.25 = 11.025538536 Reorder the terms: 9.25 + x = 11.025538536 Solving 9.25 + x = 11.025538536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + x = 11.025538536 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + x = 11.025538536 + -9.25 x = 11.025538536 + -9.25 Combine like terms: 11.025538536 + -9.25 = 1.775538536 x = 1.775538536 Simplifying x = 1.775538536Subproblem 2
x + 9.25 = -11.025538536 Simplifying x + 9.25 = -11.025538536 Reorder the terms: 9.25 + x = -11.025538536 Solving 9.25 + x = -11.025538536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + x = -11.025538536 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + x = -11.025538536 + -9.25 x = -11.025538536 + -9.25 Combine like terms: -11.025538536 + -9.25 = -20.275538536 x = -20.275538536 Simplifying x = -20.275538536Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.775538536, -20.275538536}Solution
x = {1.775538536, -20.275538536}
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