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Simplifying 4 = 20x2 + 65x + 6 Reorder the terms: 4 = 6 + 65x + 20x2 Solving 4 = 6 + 65x + 20x2 Solving for variable 'x'. Combine like terms: 4 + -6 = -2 -2 + -65x + -20x2 = 6 + 65x + 20x2 + -6 + -65x + -20x2 Reorder the terms: -2 + -65x + -20x2 = 6 + -6 + 65x + -65x + 20x2 + -20x2 Combine like terms: 6 + -6 = 0 -2 + -65x + -20x2 = 0 + 65x + -65x + 20x2 + -20x2 -2 + -65x + -20x2 = 65x + -65x + 20x2 + -20x2 Combine like terms: 65x + -65x = 0 -2 + -65x + -20x2 = 0 + 20x2 + -20x2 -2 + -65x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -2 + -65x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 65x + 20x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 65x + 20x2)' equal to zero and attempt to solve: Simplifying 2 + 65x + 20x2 = 0 Solving 2 + 65x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.1 + 3.25x + x2 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 3.25x + -0.1 + x2 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + 3.25x + x2 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 3.25x + x2 = 0.0 + -0.1 3.25x + x2 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 3.25x + x2 = -0.1 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = -0.1 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = -0.1 + 2.640625 Combine like terms: -0.1 + 2.640625 = 2.540625 2.640625 + 3.25x + x2 = 2.540625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 2.540625 Calculate the square root of the right side: 1.593933813 Break this problem into two subproblems by setting (x + 1.625) equal to 1.593933813 and -1.593933813.Subproblem 1
x + 1.625 = 1.593933813 Simplifying x + 1.625 = 1.593933813 Reorder the terms: 1.625 + x = 1.593933813 Solving 1.625 + x = 1.593933813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 1.593933813 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 1.593933813 + -1.625 x = 1.593933813 + -1.625 Combine like terms: 1.593933813 + -1.625 = -0.031066187 x = -0.031066187 Simplifying x = -0.031066187Subproblem 2
x + 1.625 = -1.593933813 Simplifying x + 1.625 = -1.593933813 Reorder the terms: 1.625 + x = -1.593933813 Solving 1.625 + x = -1.593933813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -1.593933813 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -1.593933813 + -1.625 x = -1.593933813 + -1.625 Combine like terms: -1.593933813 + -1.625 = -3.218933813 x = -3.218933813 Simplifying x = -3.218933813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.031066187, -3.218933813}Solution
x = {-0.031066187, -3.218933813}
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