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Simplifying 2x2 + -7x = 20 Reorder the terms: -7x + 2x2 = 20 Solving -7x + 2x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -7x + 2x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + -3.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -3.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -3.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3.5x + x2 = 0 + 10 -3.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -3.5x + x2 = 10 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 10 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 10 + 3.0625 Combine like terms: 10 + 3.0625 = 13.0625 3.0625 + -3.5x + x2 = 13.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 13.0625 Calculate the square root of the right side: 3.614208074 Break this problem into two subproblems by setting (x + -1.75) equal to 3.614208074 and -3.614208074.Subproblem 1
x + -1.75 = 3.614208074 Simplifying x + -1.75 = 3.614208074 Reorder the terms: -1.75 + x = 3.614208074 Solving -1.75 + x = 3.614208074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.614208074 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.614208074 + 1.75 x = 3.614208074 + 1.75 Combine like terms: 3.614208074 + 1.75 = 5.364208074 x = 5.364208074 Simplifying x = 5.364208074Subproblem 2
x + -1.75 = -3.614208074 Simplifying x + -1.75 = -3.614208074 Reorder the terms: -1.75 + x = -3.614208074 Solving -1.75 + x = -3.614208074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.614208074 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.614208074 + 1.75 x = -3.614208074 + 1.75 Combine like terms: -3.614208074 + 1.75 = -1.864208074 x = -1.864208074 Simplifying x = -1.864208074Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.364208074, -1.864208074}
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