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Simplifying X + 4 = 4X2 + 16X + 16 Reorder the terms: 4 + X = 4X2 + 16X + 16 Reorder the terms: 4 + X = 16 + 16X + 4X2 Solving 4 + X = 16 + 16X + 4X2 Solving for variable 'X'. Reorder the terms: 4 + -16 + X + -16X + -4X2 = 16 + 16X + 4X2 + -16 + -16X + -4X2 Combine like terms: 4 + -16 = -12 -12 + X + -16X + -4X2 = 16 + 16X + 4X2 + -16 + -16X + -4X2 Combine like terms: X + -16X = -15X -12 + -15X + -4X2 = 16 + 16X + 4X2 + -16 + -16X + -4X2 Reorder the terms: -12 + -15X + -4X2 = 16 + -16 + 16X + -16X + 4X2 + -4X2 Combine like terms: 16 + -16 = 0 -12 + -15X + -4X2 = 0 + 16X + -16X + 4X2 + -4X2 -12 + -15X + -4X2 = 16X + -16X + 4X2 + -4X2 Combine like terms: 16X + -16X = 0 -12 + -15X + -4X2 = 0 + 4X2 + -4X2 -12 + -15X + -4X2 = 4X2 + -4X2 Combine like terms: 4X2 + -4X2 = 0 -12 + -15X + -4X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 15X + 4X2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 15X + 4X2)' equal to zero and attempt to solve: Simplifying 12 + 15X + 4X2 = 0 Solving 12 + 15X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + 3.75X + X2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3.75X + -3 + X2 = 0 + -3 Reorder the terms: 3 + -3 + 3.75X + X2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3.75X + X2 = 0 + -3 3.75X + X2 = 0 + -3 Combine like terms: 0 + -3 = -3 3.75X + X2 = -3 The X term is 3.75X. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75X + 3.515625 + X2 = -3 + 3.515625 Reorder the terms: 3.515625 + 3.75X + X2 = -3 + 3.515625 Combine like terms: -3 + 3.515625 = 0.515625 3.515625 + 3.75X + X2 = 0.515625 Factor a perfect square on the left side: (X + 1.875)(X + 1.875) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (X + 1.875) equal to 0.718070331 and -0.718070331.Subproblem 1
X + 1.875 = 0.718070331 Simplifying X + 1.875 = 0.718070331 Reorder the terms: 1.875 + X = 0.718070331 Solving 1.875 + X = 0.718070331 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + X = 0.718070331 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + X = 0.718070331 + -1.875 X = 0.718070331 + -1.875 Combine like terms: 0.718070331 + -1.875 = -1.156929669 X = -1.156929669 Simplifying X = -1.156929669Subproblem 2
X + 1.875 = -0.718070331 Simplifying X + 1.875 = -0.718070331 Reorder the terms: 1.875 + X = -0.718070331 Solving 1.875 + X = -0.718070331 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + X = -0.718070331 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + X = -0.718070331 + -1.875 X = -0.718070331 + -1.875 Combine like terms: -0.718070331 + -1.875 = -2.593070331 X = -2.593070331 Simplifying X = -2.593070331Solution
The solution to the problem is based on the solutions from the subproblems. X = {-1.156929669, -2.593070331}Solution
X = {-1.156929669, -2.593070331}
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