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Simplifying 80 = -16x2 + 44x + 180 Reorder the terms: 80 = 180 + 44x + -16x2 Solving 80 = 180 + 44x + -16x2 Solving for variable 'x'. Combine like terms: 80 + -180 = -100 -100 + -44x + 16x2 = 180 + 44x + -16x2 + -180 + -44x + 16x2 Reorder the terms: -100 + -44x + 16x2 = 180 + -180 + 44x + -44x + -16x2 + 16x2 Combine like terms: 180 + -180 = 0 -100 + -44x + 16x2 = 0 + 44x + -44x + -16x2 + 16x2 -100 + -44x + 16x2 = 44x + -44x + -16x2 + 16x2 Combine like terms: 44x + -44x = 0 -100 + -44x + 16x2 = 0 + -16x2 + 16x2 -100 + -44x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -100 + -44x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -11x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -11x + 4x2)' equal to zero and attempt to solve: Simplifying -25 + -11x + 4x2 = 0 Solving -25 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -2.75x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -2.75x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -2.75x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -2.75x + x2 = 0 + 6.25 -2.75x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -2.75x + x2 = 6.25 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 6.25 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 6.25 + 1.890625 Combine like terms: 6.25 + 1.890625 = 8.140625 1.890625 + -2.75x + x2 = 8.140625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 8.140625 Calculate the square root of the right side: 2.853178053 Break this problem into two subproblems by setting (x + -1.375) equal to 2.853178053 and -2.853178053.Subproblem 1
x + -1.375 = 2.853178053 Simplifying x + -1.375 = 2.853178053 Reorder the terms: -1.375 + x = 2.853178053 Solving -1.375 + x = 2.853178053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.853178053 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.853178053 + 1.375 x = 2.853178053 + 1.375 Combine like terms: 2.853178053 + 1.375 = 4.228178053 x = 4.228178053 Simplifying x = 4.228178053Subproblem 2
x + -1.375 = -2.853178053 Simplifying x + -1.375 = -2.853178053 Reorder the terms: -1.375 + x = -2.853178053 Solving -1.375 + x = -2.853178053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.853178053 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.853178053 + 1.375 x = -2.853178053 + 1.375 Combine like terms: -2.853178053 + 1.375 = -1.478178053 x = -1.478178053 Simplifying x = -1.478178053Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.228178053, -1.478178053}Solution
x = {4.228178053, -1.478178053}
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