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Simplifying 2x2 + 12x + -81 = 1 Reorder the terms: -81 + 12x + 2x2 = 1 Solving -81 + 12x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -81 + -1 + 12x + 2x2 = 1 + -1 Combine like terms: -81 + -1 = -82 -82 + 12x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -82 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-41 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-41 + 6x + x2)' equal to zero and attempt to solve: Simplifying -41 + 6x + x2 = 0 Solving -41 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 6x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + 6x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 6x + x2 = 0 + 41 6x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 6x + x2 = 41 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 41 + 9 Reorder the terms: 9 + 6x + x2 = 41 + 9 Combine like terms: 41 + 9 = 50 9 + 6x + x2 = 50 Factor a perfect square on the left side: (x + 3)(x + 3) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 3) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 3 = 7.071067812 Simplifying x + 3 = 7.071067812 Reorder the terms: 3 + x = 7.071067812 Solving 3 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.071067812 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.071067812 + -3 x = 7.071067812 + -3 Combine like terms: 7.071067812 + -3 = 4.071067812 x = 4.071067812 Simplifying x = 4.071067812Subproblem 2
x + 3 = -7.071067812 Simplifying x + 3 = -7.071067812 Reorder the terms: 3 + x = -7.071067812 Solving 3 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.071067812 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.071067812 + -3 x = -7.071067812 + -3 Combine like terms: -7.071067812 + -3 = -10.071067812 x = -10.071067812 Simplifying x = -10.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.071067812, -10.071067812}Solution
x = {4.071067812, -10.071067812}
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