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Simplifying 8x2 + 42x + 42 = 0 Reorder the terms: 42 + 42x + 8x2 = 0 Solving 42 + 42x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 21x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 21x + 4x2)' equal to zero and attempt to solve: Simplifying 21 + 21x + 4x2 = 0 Solving 21 + 21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.25 + 5.25x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + 5.25x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + 5.25x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + 5.25x + x2 = 0 + -5.25 5.25x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 5.25x + x2 = -5.25 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = -5.25 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = -5.25 + 6.890625 Combine like terms: -5.25 + 6.890625 = 1.640625 6.890625 + 5.25x + x2 = 1.640625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + 2.625) equal to 1.280868846 and -1.280868846.Subproblem 1
x + 2.625 = 1.280868846 Simplifying x + 2.625 = 1.280868846 Reorder the terms: 2.625 + x = 1.280868846 Solving 2.625 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 1.280868846 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 1.280868846 + -2.625 x = 1.280868846 + -2.625 Combine like terms: 1.280868846 + -2.625 = -1.344131154 x = -1.344131154 Simplifying x = -1.344131154Subproblem 2
x + 2.625 = -1.280868846 Simplifying x + 2.625 = -1.280868846 Reorder the terms: 2.625 + x = -1.280868846 Solving 2.625 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -1.280868846 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -1.280868846 + -2.625 x = -1.280868846 + -2.625 Combine like terms: -1.280868846 + -2.625 = -3.905868846 x = -3.905868846 Simplifying x = -3.905868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.344131154, -3.905868846}Solution
x = {-1.344131154, -3.905868846}
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