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Simplifying 7x2 + 21x + -38 = 0 Reorder the terms: -38 + 21x + 7x2 = 0 Solving -38 + 21x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.428571429 + 3x + x2 = 0 Move the constant term to the right: Add '5.428571429' to each side of the equation. -5.428571429 + 3x + 5.428571429 + x2 = 0 + 5.428571429 Reorder the terms: -5.428571429 + 5.428571429 + 3x + x2 = 0 + 5.428571429 Combine like terms: -5.428571429 + 5.428571429 = 0.000000000 0.000000000 + 3x + x2 = 0 + 5.428571429 3x + x2 = 0 + 5.428571429 Combine like terms: 0 + 5.428571429 = 5.428571429 3x + x2 = 5.428571429 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 5.428571429 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 5.428571429 + 2.25 Combine like terms: 5.428571429 + 2.25 = 7.678571429 2.25 + 3x + x2 = 7.678571429 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 7.678571429 Calculate the square root of the right side: 2.771023535 Break this problem into two subproblems by setting (x + 1.5) equal to 2.771023535 and -2.771023535.Subproblem 1
x + 1.5 = 2.771023535 Simplifying x + 1.5 = 2.771023535 Reorder the terms: 1.5 + x = 2.771023535 Solving 1.5 + x = 2.771023535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.771023535 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.771023535 + -1.5 x = 2.771023535 + -1.5 Combine like terms: 2.771023535 + -1.5 = 1.271023535 x = 1.271023535 Simplifying x = 1.271023535Subproblem 2
x + 1.5 = -2.771023535 Simplifying x + 1.5 = -2.771023535 Reorder the terms: 1.5 + x = -2.771023535 Solving 1.5 + x = -2.771023535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.771023535 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.771023535 + -1.5 x = -2.771023535 + -1.5 Combine like terms: -2.771023535 + -1.5 = -4.271023535 x = -4.271023535 Simplifying x = -4.271023535Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.271023535, -4.271023535}
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