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Simplifying 2x2 + 5x + 6 = 90 Reorder the terms: 6 + 5x + 2x2 = 90 Solving 6 + 5x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: 6 + -90 + 5x + 2x2 = 90 + -90 Combine like terms: 6 + -90 = -84 -84 + 5x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -84 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -42 + 2.5x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + 2.5x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 2.5x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 2.5x + x2 = 0 + 42 2.5x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 2.5x + x2 = 42 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 = 42 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 42 + 1.5625 Combine like terms: 42 + 1.5625 = 43.5625 1.5625 + 2.5x + x2 = 43.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 43.5625 Calculate the square root of the right side: 6.600189391 Break this problem into two subproblems by setting (x + 1.25) equal to 6.600189391 and -6.600189391.Subproblem 1
x + 1.25 = 6.600189391 Simplifying x + 1.25 = 6.600189391 Reorder the terms: 1.25 + x = 6.600189391 Solving 1.25 + x = 6.600189391 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 = 6.600189391 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 6.600189391 + -1.25 x = 6.600189391 + -1.25 Combine like terms: 6.600189391 + -1.25 = 5.350189391 x = 5.350189391 Simplifying x = 5.350189391Subproblem 2
x + 1.25 = -6.600189391 Simplifying x + 1.25 = -6.600189391 Reorder the terms: 1.25 + x = -6.600189391 Solving 1.25 + x = -6.600189391 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 = -6.600189391 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -6.600189391 + -1.25 x = -6.600189391 + -1.25 Combine like terms: -6.600189391 + -1.25 = -7.850189391 x = -7.850189391 Simplifying x = -7.850189391Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.350189391, -7.850189391}
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