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Simplifying 145X2 + -20X + -20 = 0 Reorder the terms: -20 + -20X + 145X2 = 0 Solving -20 + -20X + 145X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + -4X + 29X2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + -4X + 29X2)' equal to zero and attempt to solve: Simplifying -4 + -4X + 29X2 = 0 Solving -4 + -4X + 29X2 = 0 Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. -0.1379310345 + -0.1379310345X + X2 = 0 Move the constant term to the right: Add '0.1379310345' to each side of the equation. -0.1379310345 + -0.1379310345X + 0.1379310345 + X2 = 0 + 0.1379310345 Reorder the terms: -0.1379310345 + 0.1379310345 + -0.1379310345X + X2 = 0 + 0.1379310345 Combine like terms: -0.1379310345 + 0.1379310345 = 0.0000000000 0.0000000000 + -0.1379310345X + X2 = 0 + 0.1379310345 -0.1379310345X + X2 = 0 + 0.1379310345 Combine like terms: 0 + 0.1379310345 = 0.1379310345 -0.1379310345X + X2 = 0.1379310345 The X term is -0.1379310345X. Take half its coefficient (-0.06896551725). Square it (0.004756242570) and add it to both sides. Add '0.004756242570' to each side of the equation. -0.1379310345X + 0.004756242570 + X2 = 0.1379310345 + 0.004756242570 Reorder the terms: 0.004756242570 + -0.1379310345X + X2 = 0.1379310345 + 0.004756242570 Combine like terms: 0.1379310345 + 0.004756242570 = 0.14268727707 0.004756242570 + -0.1379310345X + X2 = 0.14268727707 Factor a perfect square on the left side: (X + -0.06896551725)(X + -0.06896551725) = 0.14268727707 Calculate the square root of the right side: 0.377739695 Break this problem into two subproblems by setting (X + -0.06896551725) equal to 0.377739695 and -0.377739695.Subproblem 1
X + -0.06896551725 = 0.377739695 Simplifying X + -0.06896551725 = 0.377739695 Reorder the terms: -0.06896551725 + X = 0.377739695 Solving -0.06896551725 + X = 0.377739695 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.06896551725' to each side of the equation. -0.06896551725 + 0.06896551725 + X = 0.377739695 + 0.06896551725 Combine like terms: -0.06896551725 + 0.06896551725 = 0.00000000000 0.00000000000 + X = 0.377739695 + 0.06896551725 X = 0.377739695 + 0.06896551725 Combine like terms: 0.377739695 + 0.06896551725 = 0.44670521225 X = 0.44670521225 Simplifying X = 0.44670521225Subproblem 2
X + -0.06896551725 = -0.377739695 Simplifying X + -0.06896551725 = -0.377739695 Reorder the terms: -0.06896551725 + X = -0.377739695 Solving -0.06896551725 + X = -0.377739695 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.06896551725' to each side of the equation. -0.06896551725 + 0.06896551725 + X = -0.377739695 + 0.06896551725 Combine like terms: -0.06896551725 + 0.06896551725 = 0.00000000000 0.00000000000 + X = -0.377739695 + 0.06896551725 X = -0.377739695 + 0.06896551725 Combine like terms: -0.377739695 + 0.06896551725 = -0.30877417775 X = -0.30877417775 Simplifying X = -0.30877417775Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.44670521225, -0.30877417775}Solution
X = {0.44670521225, -0.30877417775}
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