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Simplifying 26x2 + -11x + -25 = 0 Reorder the terms: -25 + -11x + 26x2 = 0 Solving -25 + -11x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.9615384615 + -0.4230769231x + x2 = 0 Move the constant term to the right: Add '0.9615384615' to each side of the equation. -0.9615384615 + -0.4230769231x + 0.9615384615 + x2 = 0 + 0.9615384615 Reorder the terms: -0.9615384615 + 0.9615384615 + -0.4230769231x + x2 = 0 + 0.9615384615 Combine like terms: -0.9615384615 + 0.9615384615 = 0.0000000000 0.0000000000 + -0.4230769231x + x2 = 0 + 0.9615384615 -0.4230769231x + x2 = 0 + 0.9615384615 Combine like terms: 0 + 0.9615384615 = 0.9615384615 -0.4230769231x + x2 = 0.9615384615 The x term is -0.4230769231x. Take half its coefficient (-0.2115384616). Square it (0.04474852074) and add it to both sides. Add '0.04474852074' to each side of the equation. -0.4230769231x + 0.04474852074 + x2 = 0.9615384615 + 0.04474852074 Reorder the terms: 0.04474852074 + -0.4230769231x + x2 = 0.9615384615 + 0.04474852074 Combine like terms: 0.9615384615 + 0.04474852074 = 1.00628698224 0.04474852074 + -0.4230769231x + x2 = 1.00628698224 Factor a perfect square on the left side: (x + -0.2115384616)(x + -0.2115384616) = 1.00628698224 Calculate the square root of the right side: 1.003138566 Break this problem into two subproblems by setting (x + -0.2115384616) equal to 1.003138566 and -1.003138566.Subproblem 1
x + -0.2115384616 = 1.003138566 Simplifying x + -0.2115384616 = 1.003138566 Reorder the terms: -0.2115384616 + x = 1.003138566 Solving -0.2115384616 + x = 1.003138566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2115384616' to each side of the equation. -0.2115384616 + 0.2115384616 + x = 1.003138566 + 0.2115384616 Combine like terms: -0.2115384616 + 0.2115384616 = 0.0000000000 0.0000000000 + x = 1.003138566 + 0.2115384616 x = 1.003138566 + 0.2115384616 Combine like terms: 1.003138566 + 0.2115384616 = 1.2146770276 x = 1.2146770276 Simplifying x = 1.2146770276Subproblem 2
x + -0.2115384616 = -1.003138566 Simplifying x + -0.2115384616 = -1.003138566 Reorder the terms: -0.2115384616 + x = -1.003138566 Solving -0.2115384616 + x = -1.003138566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2115384616' to each side of the equation. -0.2115384616 + 0.2115384616 + x = -1.003138566 + 0.2115384616 Combine like terms: -0.2115384616 + 0.2115384616 = 0.0000000000 0.0000000000 + x = -1.003138566 + 0.2115384616 x = -1.003138566 + 0.2115384616 Combine like terms: -1.003138566 + 0.2115384616 = -0.7916001044 x = -0.7916001044 Simplifying x = -0.7916001044Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2146770276, -0.7916001044}
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