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Simplifying 8x2 + -30x + 8 = 0 Reorder the terms: 8 + -30x + 8x2 = 0 Solving 8 + -30x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -15x + 4x2) = 0 Ignore the factor 2.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 = 3.461072193 x = 3.461072193 Simplifying x = 3.461072193Subproblem 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 = 0.288927807 x = 0.288927807 Simplifying x = 0.288927807Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.461072193, 0.288927807}Solution
x = {3.461072193, 0.288927807}
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