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Simplifying 0 = 5x2 + 66x + 8 Reorder the terms: 0 = 8 + 66x + 5x2 Solving 0 = 8 + 66x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -66x + -5x2 = 8 + 66x + 5x2 + -8 + -66x + -5x2 Reorder the terms: -8 + -66x + -5x2 = 8 + -8 + 66x + -66x + 5x2 + -5x2 Combine like terms: 8 + -8 = 0 -8 + -66x + -5x2 = 0 + 66x + -66x + 5x2 + -5x2 -8 + -66x + -5x2 = 66x + -66x + 5x2 + -5x2 Combine like terms: 66x + -66x = 0 -8 + -66x + -5x2 = 0 + 5x2 + -5x2 -8 + -66x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -8 + -66x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 66x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 66x + 5x2)' equal to zero and attempt to solve: Simplifying 8 + 66x + 5x2 = 0 Solving 8 + 66x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + 13.2x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + 13.2x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + 13.2x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + 13.2x + x2 = 0 + -1.6 13.2x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 13.2x + x2 = -1.6 The x term is 13.2x. Take half its coefficient (6.6). Square it (43.56) and add it to both sides. Add '43.56' to each side of the equation. 13.2x + 43.56 + x2 = -1.6 + 43.56 Reorder the terms: 43.56 + 13.2x + x2 = -1.6 + 43.56 Combine like terms: -1.6 + 43.56 = 41.96 43.56 + 13.2x + x2 = 41.96 Factor a perfect square on the left side: (x + 6.6)(x + 6.6) = 41.96 Calculate the square root of the right side: 6.477653896 Break this problem into two subproblems by setting (x + 6.6) equal to 6.477653896 and -6.477653896.Subproblem 1
x + 6.6 = 6.477653896 Simplifying x + 6.6 = 6.477653896 Reorder the terms: 6.6 + x = 6.477653896 Solving 6.6 + x = 6.477653896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.6' to each side of the equation. 6.6 + -6.6 + x = 6.477653896 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = 6.477653896 + -6.6 x = 6.477653896 + -6.6 Combine like terms: 6.477653896 + -6.6 = -0.122346104 x = -0.122346104 Simplifying x = -0.122346104Subproblem 2
x + 6.6 = -6.477653896 Simplifying x + 6.6 = -6.477653896 Reorder the terms: 6.6 + x = -6.477653896 Solving 6.6 + x = -6.477653896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.6' to each side of the equation. 6.6 + -6.6 + x = -6.477653896 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = -6.477653896 + -6.6 x = -6.477653896 + -6.6 Combine like terms: -6.477653896 + -6.6 = -13.077653896 x = -13.077653896 Simplifying x = -13.077653896Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.122346104, -13.077653896}Solution
x = {-0.122346104, -13.077653896}
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