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Simplifying 2x2 + 5x + 1 = 20 Reorder the terms: 1 + 5x + 2x2 = 20 Solving 1 + 5x + 2x2 = 20 Solving for variable 'x'. Reorder the terms: 1 + -20 + 5x + 2x2 = 20 + -20 Combine like terms: 1 + -20 = -19 -19 + 5x + 2x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -19 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 2.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 2.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 2.5x + x2 = 0 + 9.5 2.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 2.5x + x2 = 9.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 9.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 9.5 + 1.5625 Combine like terms: 9.5 + 1.5625 = 11.0625 1.5625 + 2.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + 1.25) equal to 3.326033674 and -3.326033674.Subproblem 1
x + 1.25 = 3.326033674 Simplifying x + 1.25 = 3.326033674 Reorder the terms: 1.25 + x = 3.326033674 Solving 1.25 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.326033674 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.326033674 + -1.25 x = 3.326033674 + -1.25 Combine like terms: 3.326033674 + -1.25 = 2.076033674 x = 2.076033674 Simplifying x = 2.076033674Subproblem 2
x + 1.25 = -3.326033674 Simplifying x + 1.25 = -3.326033674 Reorder the terms: 1.25 + x = -3.326033674 Solving 1.25 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.326033674 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.326033674 + -1.25 x = -3.326033674 + -1.25 Combine like terms: -3.326033674 + -1.25 = -4.576033674 x = -4.576033674 Simplifying x = -4.576033674Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.076033674, -4.576033674}
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