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Simplifying 19X2 + 78X + -112 = 0 Reorder the terms: -112 + 78X + 19X2 = 0 Solving -112 + 78X + 19X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -5.894736842 + 4.105263158X + X2 = 0 Move the constant term to the right: Add '5.894736842' to each side of the equation. -5.894736842 + 4.105263158X + 5.894736842 + X2 = 0 + 5.894736842 Reorder the terms: -5.894736842 + 5.894736842 + 4.105263158X + X2 = 0 + 5.894736842 Combine like terms: -5.894736842 + 5.894736842 = 0.000000000 0.000000000 + 4.105263158X + X2 = 0 + 5.894736842 4.105263158X + X2 = 0 + 5.894736842 Combine like terms: 0 + 5.894736842 = 5.894736842 4.105263158X + X2 = 5.894736842 The X term is 4.105263158X. Take half its coefficient (2.052631579). Square it (4.213296399) and add it to both sides. Add '4.213296399' to each side of the equation. 4.105263158X + 4.213296399 + X2 = 5.894736842 + 4.213296399 Reorder the terms: 4.213296399 + 4.105263158X + X2 = 5.894736842 + 4.213296399 Combine like terms: 5.894736842 + 4.213296399 = 10.108033241 4.213296399 + 4.105263158X + X2 = 10.108033241 Factor a perfect square on the left side: (X + 2.052631579)(X + 2.052631579) = 10.108033241 Calculate the square root of the right side: 3.179313329 Break this problem into two subproblems by setting (X + 2.052631579) equal to 3.179313329 and -3.179313329.Subproblem 1
X + 2.052631579 = 3.179313329 Simplifying X + 2.052631579 = 3.179313329 Reorder the terms: 2.052631579 + X = 3.179313329 Solving 2.052631579 + X = 3.179313329 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.052631579' to each side of the equation. 2.052631579 + -2.052631579 + X = 3.179313329 + -2.052631579 Combine like terms: 2.052631579 + -2.052631579 = 0.000000000 0.000000000 + X = 3.179313329 + -2.052631579 X = 3.179313329 + -2.052631579 Combine like terms: 3.179313329 + -2.052631579 = 1.12668175 X = 1.12668175 Simplifying X = 1.12668175Subproblem 2
X + 2.052631579 = -3.179313329 Simplifying X + 2.052631579 = -3.179313329 Reorder the terms: 2.052631579 + X = -3.179313329 Solving 2.052631579 + X = -3.179313329 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.052631579' to each side of the equation. 2.052631579 + -2.052631579 + X = -3.179313329 + -2.052631579 Combine like terms: 2.052631579 + -2.052631579 = 0.000000000 0.000000000 + X = -3.179313329 + -2.052631579 X = -3.179313329 + -2.052631579 Combine like terms: -3.179313329 + -2.052631579 = -5.231944908 X = -5.231944908 Simplifying X = -5.231944908Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.12668175, -5.231944908}
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