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Simplifying 49x2 + 336x + 225 = 3 Reorder the terms: 225 + 336x + 49x2 = 3 Solving 225 + 336x + 49x2 = 3 Solving for variable 'x'. Reorder the terms: 225 + -3 + 336x + 49x2 = 3 + -3 Combine like terms: 225 + -3 = 222 222 + 336x + 49x2 = 3 + -3 Combine like terms: 3 + -3 = 0 222 + 336x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 4.530612245 + 6.857142857x + x2 = 0 Move the constant term to the right: Add '-4.530612245' to each side of the equation. 4.530612245 + 6.857142857x + -4.530612245 + x2 = 0 + -4.530612245 Reorder the terms: 4.530612245 + -4.530612245 + 6.857142857x + x2 = 0 + -4.530612245 Combine like terms: 4.530612245 + -4.530612245 = 0.000000000 0.000000000 + 6.857142857x + x2 = 0 + -4.530612245 6.857142857x + x2 = 0 + -4.530612245 Combine like terms: 0 + -4.530612245 = -4.530612245 6.857142857x + x2 = -4.530612245 The x term is 6.857142857x. Take half its coefficient (3.428571429). Square it (11.75510204) and add it to both sides. Add '11.75510204' to each side of the equation. 6.857142857x + 11.75510204 + x2 = -4.530612245 + 11.75510204 Reorder the terms: 11.75510204 + 6.857142857x + x2 = -4.530612245 + 11.75510204 Combine like terms: -4.530612245 + 11.75510204 = 7.224489795 11.75510204 + 6.857142857x + x2 = 7.224489795 Factor a perfect square on the left side: (x + 3.428571429)(x + 3.428571429) = 7.224489795 Calculate the square root of the right side: 2.687841103 Break this problem into two subproblems by setting (x + 3.428571429) equal to 2.687841103 and -2.687841103.Subproblem 1
x + 3.428571429 = 2.687841103 Simplifying x + 3.428571429 = 2.687841103 Reorder the terms: 3.428571429 + x = 2.687841103 Solving 3.428571429 + x = 2.687841103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.428571429' to each side of the equation. 3.428571429 + -3.428571429 + x = 2.687841103 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + x = 2.687841103 + -3.428571429 x = 2.687841103 + -3.428571429 Combine like terms: 2.687841103 + -3.428571429 = -0.740730326 x = -0.740730326 Simplifying x = -0.740730326Subproblem 2
x + 3.428571429 = -2.687841103 Simplifying x + 3.428571429 = -2.687841103 Reorder the terms: 3.428571429 + x = -2.687841103 Solving 3.428571429 + x = -2.687841103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.428571429' to each side of the equation. 3.428571429 + -3.428571429 + x = -2.687841103 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + x = -2.687841103 + -3.428571429 x = -2.687841103 + -3.428571429 Combine like terms: -2.687841103 + -3.428571429 = -6.116412532 x = -6.116412532 Simplifying x = -6.116412532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.740730326, -6.116412532}
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