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Simplifying 0 = x2 + 82x + 79 Reorder the terms: 0 = 79 + 82x + x2 Solving 0 = 79 + 82x + x2 Solving for variable 'x'. Combine like terms: 0 + -79 = -79 -79 + -82x + -1x2 = 79 + 82x + x2 + -79 + -82x + -1x2 Reorder the terms: -79 + -82x + -1x2 = 79 + -79 + 82x + -82x + x2 + -1x2 Combine like terms: 79 + -79 = 0 -79 + -82x + -1x2 = 0 + 82x + -82x + x2 + -1x2 -79 + -82x + -1x2 = 82x + -82x + x2 + -1x2 Combine like terms: 82x + -82x = 0 -79 + -82x + -1x2 = 0 + x2 + -1x2 -79 + -82x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -79 + -82x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(79 + 82x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(79 + 82x + x2)' equal to zero and attempt to solve: Simplifying 79 + 82x + x2 = 0 Solving 79 + 82x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-79' to each side of the equation. 79 + 82x + -79 + x2 = 0 + -79 Reorder the terms: 79 + -79 + 82x + x2 = 0 + -79 Combine like terms: 79 + -79 = 0 0 + 82x + x2 = 0 + -79 82x + x2 = 0 + -79 Combine like terms: 0 + -79 = -79 82x + x2 = -79 The x term is 82x. Take half its coefficient (41). Square it (1681) and add it to both sides. Add '1681' to each side of the equation. 82x + 1681 + x2 = -79 + 1681 Reorder the terms: 1681 + 82x + x2 = -79 + 1681 Combine like terms: -79 + 1681 = 1602 1681 + 82x + x2 = 1602 Factor a perfect square on the left side: (x + 41)(x + 41) = 1602 Calculate the square root of the right side: 40.024992192 Break this problem into two subproblems by setting (x + 41) equal to 40.024992192 and -40.024992192.Subproblem 1
x + 41 = 40.024992192 Simplifying x + 41 = 40.024992192 Reorder the terms: 41 + x = 40.024992192 Solving 41 + x = 40.024992192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + x = 40.024992192 + -41 Combine like terms: 41 + -41 = 0 0 + x = 40.024992192 + -41 x = 40.024992192 + -41 Combine like terms: 40.024992192 + -41 = -0.975007808 x = -0.975007808 Simplifying x = -0.975007808Subproblem 2
x + 41 = -40.024992192 Simplifying x + 41 = -40.024992192 Reorder the terms: 41 + x = -40.024992192 Solving 41 + x = -40.024992192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + x = -40.024992192 + -41 Combine like terms: 41 + -41 = 0 0 + x = -40.024992192 + -41 x = -40.024992192 + -41 Combine like terms: -40.024992192 + -41 = -81.024992192 x = -81.024992192 Simplifying x = -81.024992192Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.975007808, -81.024992192}Solution
x = {-0.975007808, -81.024992192}
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