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Simplifying 2x2 + 5x + -3 = 23 Reorder the terms: -3 + 5x + 2x2 = 23 Solving -3 + 5x + 2x2 = 23 Solving for variable 'x'. Reorder the terms: -3 + -23 + 5x + 2x2 = 23 + -23 Combine like terms: -3 + -23 = -26 -26 + 5x + 2x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -26 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + 2.5x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 2.5x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 2.5x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2.5x + x2 = 0 + 13 2.5x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 2.5x + x2 = 13 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 = 13 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 13 + 1.5625 Combine like terms: 13 + 1.5625 = 14.5625 1.5625 + 2.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + 1.25) equal to 3.816084381 and -3.816084381.Subproblem 1
x + 1.25 = 3.816084381 Simplifying x + 1.25 = 3.816084381 Reorder the terms: 1.25 + x = 3.816084381 Solving 1.25 + x = 3.816084381 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 = 3.816084381 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.816084381 + -1.25 x = 3.816084381 + -1.25 Combine like terms: 3.816084381 + -1.25 = 2.566084381 x = 2.566084381 Simplifying x = 2.566084381Subproblem 2
x + 1.25 = -3.816084381 Simplifying x + 1.25 = -3.816084381 Reorder the terms: 1.25 + x = -3.816084381 Solving 1.25 + x = -3.816084381 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 = -3.816084381 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.816084381 + -1.25 x = -3.816084381 + -1.25 Combine like terms: -3.816084381 + -1.25 = -5.066084381 x = -5.066084381 Simplifying x = -5.066084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.566084381, -5.066084381}
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