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Simplifying 2x2 + 8x + -91 = 0 Reorder the terms: -91 + 8x + 2x2 = 0 Solving -91 + 8x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -45.5 + 4x + x2 = 0 Move the constant term to the right: Add '45.5' to each side of the equation. -45.5 + 4x + 45.5 + x2 = 0 + 45.5 Reorder the terms: -45.5 + 45.5 + 4x + x2 = 0 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + 4x + x2 = 0 + 45.5 4x + x2 = 0 + 45.5 Combine like terms: 0 + 45.5 = 45.5 4x + x2 = 45.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 45.5 + 4 Reorder the terms: 4 + 4x + x2 = 45.5 + 4 Combine like terms: 45.5 + 4 = 49.5 4 + 4x + x2 = 49.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 49.5 Calculate the square root of the right side: 7.03562364 Break this problem into two subproblems by setting (x + 2) equal to 7.03562364 and -7.03562364.Subproblem 1
x + 2 = 7.03562364 Simplifying x + 2 = 7.03562364 Reorder the terms: 2 + x = 7.03562364 Solving 2 + x = 7.03562364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 7.03562364 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.03562364 + -2 x = 7.03562364 + -2 Combine like terms: 7.03562364 + -2 = 5.03562364 x = 5.03562364 Simplifying x = 5.03562364Subproblem 2
x + 2 = -7.03562364 Simplifying x + 2 = -7.03562364 Reorder the terms: 2 + x = -7.03562364 Solving 2 + x = -7.03562364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -7.03562364 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.03562364 + -2 x = -7.03562364 + -2 Combine like terms: -7.03562364 + -2 = -9.03562364 x = -9.03562364 Simplifying x = -9.03562364Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.03562364, -9.03562364}
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