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Simplifying 5x + 3x2 = 25 Solving 5x + 3x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 5x + 3x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + 1.666666667x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + 1.666666667x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 8.333333333 1.666666667x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 1.666666667x + x2 = 8.333333333 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 8.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 8.333333333 + 0.6944444447 Combine like terms: 8.333333333 + 0.6944444447 = 9.0277777777 0.6944444447 + 1.666666667x + x2 = 9.0277777777 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 9.0277777777 Calculate the square root of the right side: 3.004626063 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 3.004626063 and -3.004626063.Subproblem 1
x + 0.8333333335 = 3.004626063 Simplifying x + 0.8333333335 = 3.004626063 Reorder the terms: 0.8333333335 + x = 3.004626063 Solving 0.8333333335 + x = 3.004626063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 3.004626063 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 3.004626063 + -0.8333333335 x = 3.004626063 + -0.8333333335 Combine like terms: 3.004626063 + -0.8333333335 = 2.1712927295 x = 2.1712927295 Simplifying x = 2.1712927295Subproblem 2
x + 0.8333333335 = -3.004626063 Simplifying x + 0.8333333335 = -3.004626063 Reorder the terms: 0.8333333335 + x = -3.004626063 Solving 0.8333333335 + x = -3.004626063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -3.004626063 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -3.004626063 + -0.8333333335 x = -3.004626063 + -0.8333333335 Combine like terms: -3.004626063 + -0.8333333335 = -3.8379593965 x = -3.8379593965 Simplifying x = -3.8379593965Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1712927295, -3.8379593965}
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