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Simplifying 2x2 + 6.5x = 21 Reorder the terms: 6.5x + 2x2 = 21 Solving 6.5x + 2x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 6.5x + 2x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 6.5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + 3.25x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 3.25x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 3.25x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 3.25x + x2 = 0 + 10.5 3.25x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 3.25x + x2 = 10.5 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 10.5 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 10.5 + 2.640625 Combine like terms: 10.5 + 2.640625 = 13.140625 2.640625 + 3.25x + x2 = 13.140625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 13.140625 Calculate the square root of the right side: 3.625 Break this problem into two subproblems by setting (x + 1.625) equal to 3.625 and -3.625.Subproblem 1
x + 1.625 = 3.625 Simplifying x + 1.625 = 3.625 Reorder the terms: 1.625 + x = 3.625 Solving 1.625 + x = 3.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 3.625 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 3.625 + -1.625 x = 3.625 + -1.625 Combine like terms: 3.625 + -1.625 = 2 x = 2 Simplifying x = 2Subproblem 2
x + 1.625 = -3.625 Simplifying x + 1.625 = -3.625 Reorder the terms: 1.625 + x = -3.625 Solving 1.625 + x = -3.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -3.625 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -3.625 + -1.625 x = -3.625 + -1.625 Combine like terms: -3.625 + -1.625 = -5.25 x = -5.25 Simplifying x = -5.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -5.25}
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