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Simplifying 13.44x2 + -1x + -2 = 0 Reorder the terms: -2 + -1x + 13.44x2 = 0 Solving -2 + -1x + 13.44x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13.44 the coefficient of the squared term: Divide each side by '13.44'. -0.1488095238 + -0.0744047619x + x2 = 0 Move the constant term to the right: Add '0.1488095238' to each side of the equation. -0.1488095238 + -0.0744047619x + 0.1488095238 + x2 = 0 + 0.1488095238 Reorder the terms: -0.1488095238 + 0.1488095238 + -0.0744047619x + x2 = 0 + 0.1488095238 Combine like terms: -0.1488095238 + 0.1488095238 = 0.0000000000 0.0000000000 + -0.0744047619x + x2 = 0 + 0.1488095238 -0.0744047619x + x2 = 0 + 0.1488095238 Combine like terms: 0 + 0.1488095238 = 0.1488095238 -0.0744047619x + x2 = 0.1488095238 The x term is -0.0744047619x. Take half its coefficient (-0.03720238095). Square it (0.001384017148) and add it to both sides. Add '0.001384017148' to each side of the equation. -0.0744047619x + 0.001384017148 + x2 = 0.1488095238 + 0.001384017148 Reorder the terms: 0.001384017148 + -0.0744047619x + x2 = 0.1488095238 + 0.001384017148 Combine like terms: 0.1488095238 + 0.001384017148 = 0.150193540948 0.001384017148 + -0.0744047619x + x2 = 0.150193540948 Factor a perfect square on the left side: (x + -0.03720238095)(x + -0.03720238095) = 0.150193540948 Calculate the square root of the right side: 0.387548114 Break this problem into two subproblems by setting (x + -0.03720238095) equal to 0.387548114 and -0.387548114.Subproblem 1
x + -0.03720238095 = 0.387548114 Simplifying x + -0.03720238095 = 0.387548114 Reorder the terms: -0.03720238095 + x = 0.387548114 Solving -0.03720238095 + x = 0.387548114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03720238095' to each side of the equation. -0.03720238095 + 0.03720238095 + x = 0.387548114 + 0.03720238095 Combine like terms: -0.03720238095 + 0.03720238095 = 0.00000000000 0.00000000000 + x = 0.387548114 + 0.03720238095 x = 0.387548114 + 0.03720238095 Combine like terms: 0.387548114 + 0.03720238095 = 0.42475049495 x = 0.42475049495 Simplifying x = 0.42475049495Subproblem 2
x + -0.03720238095 = -0.387548114 Simplifying x + -0.03720238095 = -0.387548114 Reorder the terms: -0.03720238095 + x = -0.387548114 Solving -0.03720238095 + x = -0.387548114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03720238095' to each side of the equation. -0.03720238095 + 0.03720238095 + x = -0.387548114 + 0.03720238095 Combine like terms: -0.03720238095 + 0.03720238095 = 0.00000000000 0.00000000000 + x = -0.387548114 + 0.03720238095 x = -0.387548114 + 0.03720238095 Combine like terms: -0.387548114 + 0.03720238095 = -0.35034573305 x = -0.35034573305 Simplifying x = -0.35034573305Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.42475049495, -0.35034573305}
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