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Simplifying -4X2 + -16X + 28 = 0 Reorder the terms: 28 + -16X + -4X2 = 0 Solving 28 + -16X + -4X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -4X + -1X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -4X + -1X2)' equal to zero and attempt to solve: Simplifying 7 + -4X + -1X2 = 0 Solving 7 + -4X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + 4X + X2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 4X + 7 + X2 = 0 + 7 Reorder the terms: -7 + 7 + 4X + X2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4X + X2 = 0 + 7 4X + X2 = 0 + 7 Combine like terms: 0 + 7 = 7 4X + X2 = 7 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 7 + 4 Reorder the terms: 4 + 4X + X2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + 4X + X2 = 11 Factor a perfect square on the left side: (X + 2)(X + 2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (X + 2) equal to 3.31662479 and -3.31662479.Subproblem 1
X + 2 = 3.31662479 Simplifying X + 2 = 3.31662479 Reorder the terms: 2 + X = 3.31662479 Solving 2 + X = 3.31662479 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + X = 3.31662479 + -2 X = 3.31662479 + -2 Combine like terms: 3.31662479 + -2 = 1.31662479 X = 1.31662479 Simplifying X = 1.31662479Subproblem 2
X + 2 = -3.31662479 Simplifying X + 2 = -3.31662479 Reorder the terms: 2 + X = -3.31662479 Solving 2 + X = -3.31662479 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + X = -3.31662479 + -2 X = -3.31662479 + -2 Combine like terms: -3.31662479 + -2 = -5.31662479 X = -5.31662479 Simplifying X = -5.31662479Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.31662479, -5.31662479}Solution
X = {1.31662479, -5.31662479}
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