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Simplifying (3x + 61)(7x) = 29 Reorder the terms: (61 + 3x)(7x) = 29 Remove parenthesis around (7x) (61 + 3x) * 7x = 29 Reorder the terms for easier multiplication: 7x(61 + 3x) = 29 (61 * 7x + 3x * 7x) = 29 (427x + 21x2) = 29 Solving 427x + 21x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + 427x + 21x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 427x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.380952381 + 20.33333333x + x2 = 0 Move the constant term to the right: Add '1.380952381' to each side of the equation. -1.380952381 + 20.33333333x + 1.380952381 + x2 = 0 + 1.380952381 Reorder the terms: -1.380952381 + 1.380952381 + 20.33333333x + x2 = 0 + 1.380952381 Combine like terms: -1.380952381 + 1.380952381 = 0.000000000 0.000000000 + 20.33333333x + x2 = 0 + 1.380952381 20.33333333x + x2 = 0 + 1.380952381 Combine like terms: 0 + 1.380952381 = 1.380952381 20.33333333x + x2 = 1.380952381 The x term is 20.33333333x. Take half its coefficient (10.16666667). Square it (103.3611112) and add it to both sides. Add '103.3611112' to each side of the equation. 20.33333333x + 103.3611112 + x2 = 1.380952381 + 103.3611112 Reorder the terms: 103.3611112 + 20.33333333x + x2 = 1.380952381 + 103.3611112 Combine like terms: 1.380952381 + 103.3611112 = 104.742063581 103.3611112 + 20.33333333x + x2 = 104.742063581 Factor a perfect square on the left side: (x + 10.16666667)(x + 10.16666667) = 104.742063581 Calculate the square root of the right side: 10.234357018 Break this problem into two subproblems by setting (x + 10.16666667) equal to 10.234357018 and -10.234357018.Subproblem 1
x + 10.16666667 = 10.234357018 Simplifying x + 10.16666667 = 10.234357018 Reorder the terms: 10.16666667 + x = 10.234357018 Solving 10.16666667 + x = 10.234357018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.16666667' to each side of the equation. 10.16666667 + -10.16666667 + x = 10.234357018 + -10.16666667 Combine like terms: 10.16666667 + -10.16666667 = 0.00000000 0.00000000 + x = 10.234357018 + -10.16666667 x = 10.234357018 + -10.16666667 Combine like terms: 10.234357018 + -10.16666667 = 0.067690348 x = 0.067690348 Simplifying x = 0.067690348Subproblem 2
x + 10.16666667 = -10.234357018 Simplifying x + 10.16666667 = -10.234357018 Reorder the terms: 10.16666667 + x = -10.234357018 Solving 10.16666667 + x = -10.234357018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.16666667' to each side of the equation. 10.16666667 + -10.16666667 + x = -10.234357018 + -10.16666667 Combine like terms: 10.16666667 + -10.16666667 = 0.00000000 0.00000000 + x = -10.234357018 + -10.16666667 x = -10.234357018 + -10.16666667 Combine like terms: -10.234357018 + -10.16666667 = -20.401023688 x = -20.401023688 Simplifying x = -20.401023688Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.067690348, -20.401023688}
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