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Simplifying 4X2 + -12X + -19 = 0 Reorder the terms: -19 + -12X + 4X2 = 0 Solving -19 + -12X + 4X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + -3X + X2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -3X + 4.75 + X2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -3X + X2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -3X + X2 = 0 + 4.75 -3X + X2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -3X + X2 = 4.75 The X term is -3X. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3X + 2.25 + X2 = 4.75 + 2.25 Reorder the terms: 2.25 + -3X + X2 = 4.75 + 2.25 Combine like terms: 4.75 + 2.25 = 7 2.25 + -3X + X2 = 7 Factor a perfect square on the left side: (X + -1.5)(X + -1.5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (X + -1.5) equal to 2.645751311 and -2.645751311.Subproblem 1
X + -1.5 = 2.645751311 Simplifying X + -1.5 = 2.645751311 Reorder the terms: -1.5 + X = 2.645751311 Solving -1.5 + X = 2.645751311 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + X = 2.645751311 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = 2.645751311 + 1.5 X = 2.645751311 + 1.5 Combine like terms: 2.645751311 + 1.5 = 4.145751311 X = 4.145751311 Simplifying X = 4.145751311Subproblem 2
X + -1.5 = -2.645751311 Simplifying X + -1.5 = -2.645751311 Reorder the terms: -1.5 + X = -2.645751311 Solving -1.5 + X = -2.645751311 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + X = -2.645751311 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = -2.645751311 + 1.5 X = -2.645751311 + 1.5 Combine like terms: -2.645751311 + 1.5 = -1.145751311 X = -1.145751311 Simplifying X = -1.145751311Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.145751311, -1.145751311}
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