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Simplifying x * 3x + 2(17x) = 42 Reorder the terms for easier multiplication: 3x * x + 2(17x) = 42 Multiply x * x 3x2 + 2(17x) = 42 Remove parenthesis around (17x) 3x2 + 2 * 17x = 42 Multiply 2 * 17 3x2 + 34x = 42 Reorder the terms: 34x + 3x2 = 42 Solving 34x + 3x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 34x + 3x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 34x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14 + 11.33333333x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 11.33333333x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 11.33333333x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 11.33333333x + x2 = 0 + 14 11.33333333x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 11.33333333x + x2 = 14 The x term is 11.33333333x. Take half its coefficient (5.666666665). Square it (32.11111109) and add it to both sides. Add '32.11111109' to each side of the equation. 11.33333333x + 32.11111109 + x2 = 14 + 32.11111109 Reorder the terms: 32.11111109 + 11.33333333x + x2 = 14 + 32.11111109 Combine like terms: 14 + 32.11111109 = 46.11111109 32.11111109 + 11.33333333x + x2 = 46.11111109 Factor a perfect square on the left side: (x + 5.666666665)(x + 5.666666665) = 46.11111109 Calculate the square root of the right side: 6.790516261 Break this problem into two subproblems by setting (x + 5.666666665) equal to 6.790516261 and -6.790516261.Subproblem 1
x + 5.666666665 = 6.790516261 Simplifying x + 5.666666665 = 6.790516261 Reorder the terms: 5.666666665 + x = 6.790516261 Solving 5.666666665 + x = 6.790516261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.666666665' to each side of the equation. 5.666666665 + -5.666666665 + x = 6.790516261 + -5.666666665 Combine like terms: 5.666666665 + -5.666666665 = 0.000000000 0.000000000 + x = 6.790516261 + -5.666666665 x = 6.790516261 + -5.666666665 Combine like terms: 6.790516261 + -5.666666665 = 1.123849596 x = 1.123849596 Simplifying x = 1.123849596Subproblem 2
x + 5.666666665 = -6.790516261 Simplifying x + 5.666666665 = -6.790516261 Reorder the terms: 5.666666665 + x = -6.790516261 Solving 5.666666665 + x = -6.790516261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.666666665' to each side of the equation. 5.666666665 + -5.666666665 + x = -6.790516261 + -5.666666665 Combine like terms: 5.666666665 + -5.666666665 = 0.000000000 0.000000000 + x = -6.790516261 + -5.666666665 x = -6.790516261 + -5.666666665 Combine like terms: -6.790516261 + -5.666666665 = -12.457182926 x = -12.457182926 Simplifying x = -12.457182926Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.123849596, -12.457182926}
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