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Simplifying 7.56X2 + 2.64X = 5.21 Reorder the terms: 2.64X + 7.56X2 = 5.21 Solving 2.64X + 7.56X2 = 5.21 Solving for variable 'X'. Reorder the terms: -5.21 + 2.64X + 7.56X2 = 5.21 + -5.21 Combine like terms: 5.21 + -5.21 = 0.00 -5.21 + 2.64X + 7.56X2 = 0.00 Begin completing the square. Divide all terms by 7.56 the coefficient of the squared term: Divide each side by '7.56'. -0.6891534392 + 0.3492063492X + X2 = 0 Move the constant term to the right: Add '0.6891534392' to each side of the equation. -0.6891534392 + 0.3492063492X + 0.6891534392 + X2 = 0 + 0.6891534392 Reorder the terms: -0.6891534392 + 0.6891534392 + 0.3492063492X + X2 = 0 + 0.6891534392 Combine like terms: -0.6891534392 + 0.6891534392 = 0.0000000000 0.0000000000 + 0.3492063492X + X2 = 0 + 0.6891534392 0.3492063492X + X2 = 0 + 0.6891534392 Combine like terms: 0 + 0.6891534392 = 0.6891534392 0.3492063492X + X2 = 0.6891534392 The X term is 0.3492063492X. Take half its coefficient (0.1746031746). Square it (0.03048626858) and add it to both sides. Add '0.03048626858' to each side of the equation. 0.3492063492X + 0.03048626858 + X2 = 0.6891534392 + 0.03048626858 Reorder the terms: 0.03048626858 + 0.3492063492X + X2 = 0.6891534392 + 0.03048626858 Combine like terms: 0.6891534392 + 0.03048626858 = 0.71963970778 0.03048626858 + 0.3492063492X + X2 = 0.71963970778 Factor a perfect square on the left side: (X + 0.1746031746)(X + 0.1746031746) = 0.71963970778 Calculate the square root of the right side: 0.848315807 Break this problem into two subproblems by setting (X + 0.1746031746) equal to 0.848315807 and -0.848315807.Subproblem 1
X + 0.1746031746 = 0.848315807 Simplifying X + 0.1746031746 = 0.848315807 Reorder the terms: 0.1746031746 + X = 0.848315807 Solving 0.1746031746 + X = 0.848315807 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.1746031746' to each side of the equation. 0.1746031746 + -0.1746031746 + X = 0.848315807 + -0.1746031746 Combine like terms: 0.1746031746 + -0.1746031746 = 0.0000000000 0.0000000000 + X = 0.848315807 + -0.1746031746 X = 0.848315807 + -0.1746031746 Combine like terms: 0.848315807 + -0.1746031746 = 0.6737126324 X = 0.6737126324 Simplifying X = 0.6737126324Subproblem 2
X + 0.1746031746 = -0.848315807 Simplifying X + 0.1746031746 = -0.848315807 Reorder the terms: 0.1746031746 + X = -0.848315807 Solving 0.1746031746 + X = -0.848315807 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.1746031746' to each side of the equation. 0.1746031746 + -0.1746031746 + X = -0.848315807 + -0.1746031746 Combine like terms: 0.1746031746 + -0.1746031746 = 0.0000000000 0.0000000000 + X = -0.848315807 + -0.1746031746 X = -0.848315807 + -0.1746031746 Combine like terms: -0.848315807 + -0.1746031746 = -1.0229189816 X = -1.0229189816 Simplifying X = -1.0229189816Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.6737126324, -1.0229189816}
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