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Simplifying 38X2 + 3X + -45 = 0 Reorder the terms: -45 + 3X + 38X2 = 0 Solving -45 + 3X + 38X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 38 the coefficient of the squared term: Divide each side by '38'. -1.184210526 + 0.07894736842X + X2 = 0 Move the constant term to the right: Add '1.184210526' to each side of the equation. -1.184210526 + 0.07894736842X + 1.184210526 + X2 = 0 + 1.184210526 Reorder the terms: -1.184210526 + 1.184210526 + 0.07894736842X + X2 = 0 + 1.184210526 Combine like terms: -1.184210526 + 1.184210526 = 0.000000000 0.000000000 + 0.07894736842X + X2 = 0 + 1.184210526 0.07894736842X + X2 = 0 + 1.184210526 Combine like terms: 0 + 1.184210526 = 1.184210526 0.07894736842X + X2 = 1.184210526 The X term is 0.07894736842X. Take half its coefficient (0.03947368421). Square it (0.001558171745) and add it to both sides. Add '0.001558171745' to each side of the equation. 0.07894736842X + 0.001558171745 + X2 = 1.184210526 + 0.001558171745 Reorder the terms: 0.001558171745 + 0.07894736842X + X2 = 1.184210526 + 0.001558171745 Combine like terms: 1.184210526 + 0.001558171745 = 1.185768697745 0.001558171745 + 0.07894736842X + X2 = 1.185768697745 Factor a perfect square on the left side: (X + 0.03947368421)(X + 0.03947368421) = 1.185768697745 Calculate the square root of the right side: 1.08893007 Break this problem into two subproblems by setting (X + 0.03947368421) equal to 1.08893007 and -1.08893007.Subproblem 1
X + 0.03947368421 = 1.08893007 Simplifying X + 0.03947368421 = 1.08893007 Reorder the terms: 0.03947368421 + X = 1.08893007 Solving 0.03947368421 + X = 1.08893007 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.03947368421' to each side of the equation. 0.03947368421 + -0.03947368421 + X = 1.08893007 + -0.03947368421 Combine like terms: 0.03947368421 + -0.03947368421 = 0.00000000000 0.00000000000 + X = 1.08893007 + -0.03947368421 X = 1.08893007 + -0.03947368421 Combine like terms: 1.08893007 + -0.03947368421 = 1.04945638579 X = 1.04945638579 Simplifying X = 1.04945638579Subproblem 2
X + 0.03947368421 = -1.08893007 Simplifying X + 0.03947368421 = -1.08893007 Reorder the terms: 0.03947368421 + X = -1.08893007 Solving 0.03947368421 + X = -1.08893007 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.03947368421' to each side of the equation. 0.03947368421 + -0.03947368421 + X = -1.08893007 + -0.03947368421 Combine like terms: 0.03947368421 + -0.03947368421 = 0.00000000000 0.00000000000 + X = -1.08893007 + -0.03947368421 X = -1.08893007 + -0.03947368421 Combine like terms: -1.08893007 + -0.03947368421 = -1.12840375421 X = -1.12840375421 Simplifying X = -1.12840375421Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.04945638579, -1.12840375421}
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