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Simplifying 5x2 + -26x + -11 = 0 Reorder the terms: -11 + -26x + 5x2 = 0 Solving -11 + -26x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + -5.2x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -5.2x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -5.2x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -5.2x + x2 = 0 + 2.2 -5.2x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -5.2x + x2 = 2.2 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = 2.2 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = 2.2 + 6.76 Combine like terms: 2.2 + 6.76 = 8.96 6.76 + -5.2x + x2 = 8.96 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 8.96 Calculate the square root of the right side: 2.993325909 Break this problem into two subproblems by setting (x + -2.6) equal to 2.993325909 and -2.993325909.Subproblem 1
x + -2.6 = 2.993325909 Simplifying x + -2.6 = 2.993325909 Reorder the terms: -2.6 + x = 2.993325909 Solving -2.6 + x = 2.993325909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 2.993325909 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 2.993325909 + 2.6 x = 2.993325909 + 2.6 Combine like terms: 2.993325909 + 2.6 = 5.593325909 x = 5.593325909 Simplifying x = 5.593325909Subproblem 2
x + -2.6 = -2.993325909 Simplifying x + -2.6 = -2.993325909 Reorder the terms: -2.6 + x = -2.993325909 Solving -2.6 + x = -2.993325909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -2.993325909 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -2.993325909 + 2.6 x = -2.993325909 + 2.6 Combine like terms: -2.993325909 + 2.6 = -0.393325909 x = -0.393325909 Simplifying x = -0.393325909Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.593325909, -0.393325909}
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