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Simplifying 0 = -16x2 + 272x + -20 Reorder the terms: 0 = -20 + 272x + -16x2 Solving 0 = -20 + 272x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 20 = 20 20 + -272x + 16x2 = -20 + 272x + -16x2 + 20 + -272x + 16x2 Reorder the terms: 20 + -272x + 16x2 = -20 + 20 + 272x + -272x + -16x2 + 16x2 Combine like terms: -20 + 20 = 0 20 + -272x + 16x2 = 0 + 272x + -272x + -16x2 + 16x2 20 + -272x + 16x2 = 272x + -272x + -16x2 + 16x2 Combine like terms: 272x + -272x = 0 20 + -272x + 16x2 = 0 + -16x2 + 16x2 20 + -272x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 20 + -272x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -68x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -68x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + -68x + 4x2 = 0 Solving 5 + -68x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -17x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -17x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -17x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -17x + x2 = 0 + -1.25 -17x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -17x + x2 = -1.25 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -1.25 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -1.25 + 72.25 Combine like terms: -1.25 + 72.25 = 71 72.25 + -17x + x2 = 71 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + -8.5) equal to 8.426149773 and -8.426149773.Subproblem 1
x + -8.5 = 8.426149773 Simplifying x + -8.5 = 8.426149773 Reorder the terms: -8.5 + x = 8.426149773 Solving -8.5 + x = 8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 8.426149773 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.426149773 + 8.5 x = 8.426149773 + 8.5 Combine like terms: 8.426149773 + 8.5 = 16.926149773 x = 16.926149773 Simplifying x = 16.926149773Subproblem 2
x + -8.5 = -8.426149773 Simplifying x + -8.5 = -8.426149773 Reorder the terms: -8.5 + x = -8.426149773 Solving -8.5 + x = -8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -8.426149773 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.426149773 + 8.5 x = -8.426149773 + 8.5 Combine like terms: -8.426149773 + 8.5 = 0.073850227 x = 0.073850227 Simplifying x = 0.073850227Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.926149773, 0.073850227}Solution
x = {16.926149773, 0.073850227}
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