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Simplifying 3x(7 + -1x) = 29 (7 * 3x + -1x * 3x) = 29 (21x + -3x2) = 29 Solving 21x + -3x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + 21x + -3x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 21x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 9.666666667 + -7x + x2 = 0 Move the constant term to the right: Add '-9.666666667' to each side of the equation. 9.666666667 + -7x + -9.666666667 + x2 = 0 + -9.666666667 Reorder the terms: 9.666666667 + -9.666666667 + -7x + x2 = 0 + -9.666666667 Combine like terms: 9.666666667 + -9.666666667 = 0.000000000 0.000000000 + -7x + x2 = 0 + -9.666666667 -7x + x2 = 0 + -9.666666667 Combine like terms: 0 + -9.666666667 = -9.666666667 -7x + x2 = -9.666666667 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -9.666666667 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -9.666666667 + 12.25 Combine like terms: -9.666666667 + 12.25 = 2.583333333 12.25 + -7x + x2 = 2.583333333 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 2.583333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (x + -3.5) equal to 1.607275127 and -1.607275127.Subproblem 1
x + -3.5 = 1.607275127 Simplifying x + -3.5 = 1.607275127 Reorder the terms: -3.5 + x = 1.607275127 Solving -3.5 + x = 1.607275127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.607275127 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.607275127 + 3.5 x = 1.607275127 + 3.5 Combine like terms: 1.607275127 + 3.5 = 5.107275127 x = 5.107275127 Simplifying x = 5.107275127Subproblem 2
x + -3.5 = -1.607275127 Simplifying x + -3.5 = -1.607275127 Reorder the terms: -3.5 + x = -1.607275127 Solving -3.5 + x = -1.607275127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.607275127 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.607275127 + 3.5 x = -1.607275127 + 3.5 Combine like terms: -1.607275127 + 3.5 = 1.892724873 x = 1.892724873 Simplifying x = 1.892724873Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.107275127, 1.892724873}
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