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Simplifying 2x2 + -20x = 49 Reorder the terms: -20x + 2x2 = 49 Solving -20x + 2x2 = 49 Solving for variable 'x'. Reorder the terms: -49 + -20x + 2x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24.5 + -10x + x2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + -10x + 24.5 + x2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + -10x + x2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + -10x + x2 = 0 + 24.5 -10x + x2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 -10x + x2 = 24.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 24.5 + 25 Reorder the terms: 25 + -10x + x2 = 24.5 + 25 Combine like terms: 24.5 + 25 = 49.5 25 + -10x + x2 = 49.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 49.5 Calculate the square root of the right side: 7.03562364 Break this problem into two subproblems by setting (x + -5) equal to 7.03562364 and -7.03562364.Subproblem 1
x + -5 = 7.03562364 Simplifying x + -5 = 7.03562364 Reorder the terms: -5 + x = 7.03562364 Solving -5 + x = 7.03562364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.03562364 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.03562364 + 5 x = 7.03562364 + 5 Combine like terms: 7.03562364 + 5 = 12.03562364 x = 12.03562364 Simplifying x = 12.03562364Subproblem 2
x + -5 = -7.03562364 Simplifying x + -5 = -7.03562364 Reorder the terms: -5 + x = -7.03562364 Solving -5 + x = -7.03562364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.03562364 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.03562364 + 5 x = -7.03562364 + 5 Combine like terms: -7.03562364 + 5 = -2.03562364 x = -2.03562364 Simplifying x = -2.03562364Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.03562364, -2.03562364}
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