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Simplifying 0 = 16x2 + 60x + 16 Reorder the terms: 0 = 16 + 60x + 16x2 Solving 0 = 16 + 60x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -16 = -16 -16 + -60x + -16x2 = 16 + 60x + 16x2 + -16 + -60x + -16x2 Reorder the terms: -16 + -60x + -16x2 = 16 + -16 + 60x + -60x + 16x2 + -16x2 Combine like terms: 16 + -16 = 0 -16 + -60x + -16x2 = 0 + 60x + -60x + 16x2 + -16x2 -16 + -60x + -16x2 = 60x + -60x + 16x2 + -16x2 Combine like terms: 60x + -60x = 0 -16 + -60x + -16x2 = 0 + 16x2 + -16x2 -16 + -60x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -16 + -60x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(4 + 15x + 4x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(4 + 15x + 4x2)' equal to zero and attempt to solve: Simplifying 4 + 15x + 4x2 = 0 Solving 4 + 15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 3.75x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3.75x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 3.75x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3.75x + x2 = 0 + -1 3.75x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3.75x + x2 = -1 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 = -1 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = -1 + 3.515625 Combine like terms: -1 + 3.515625 = 2.515625 3.515625 + 3.75x + x2 = 2.515625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (x + 1.875) equal to 1.586072193 and -1.586072193.Subproblem 1
x + 1.875 = 1.586072193 Simplifying x + 1.875 = 1.586072193 Reorder the terms: 1.875 + x = 1.586072193 Solving 1.875 + x = 1.586072193 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 = 1.586072193 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 1.586072193 + -1.875 x = 1.586072193 + -1.875 Combine like terms: 1.586072193 + -1.875 = -0.288927807 x = -0.288927807 Simplifying x = -0.288927807Subproblem 2
x + 1.875 = -1.586072193 Simplifying x + 1.875 = -1.586072193 Reorder the terms: 1.875 + x = -1.586072193 Solving 1.875 + x = -1.586072193 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 = -1.586072193 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -1.586072193 + -1.875 x = -1.586072193 + -1.875 Combine like terms: -1.586072193 + -1.875 = -3.461072193 x = -3.461072193 Simplifying x = -3.461072193Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.288927807, -3.461072193}Solution
x = {-0.288927807, -3.461072193}
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