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Simplifying 7(x + 5) * x = 10 Reorder the terms: 7(5 + x) * x = 10 Reorder the terms for easier multiplication: 7x(5 + x) = 10 (5 * 7x + x * 7x) = 10 (35x + 7x2) = 10 Solving 35x + 7x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 35x + 7x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 35x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + 5x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 5x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 5x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 5x + x2 = 0 + 1.428571429 5x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 5x + x2 = 1.428571429 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 1.428571429 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1.428571429 + 6.25 Combine like terms: 1.428571429 + 6.25 = 7.678571429 6.25 + 5x + x2 = 7.678571429 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 7.678571429 Calculate the square root of the right side: 2.771023535 Break this problem into two subproblems by setting (x + 2.5) equal to 2.771023535 and -2.771023535.Subproblem 1
x + 2.5 = 2.771023535 Simplifying x + 2.5 = 2.771023535 Reorder the terms: 2.5 + x = 2.771023535 Solving 2.5 + x = 2.771023535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.771023535 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.771023535 + -2.5 x = 2.771023535 + -2.5 Combine like terms: 2.771023535 + -2.5 = 0.271023535 x = 0.271023535 Simplifying x = 0.271023535Subproblem 2
x + 2.5 = -2.771023535 Simplifying x + 2.5 = -2.771023535 Reorder the terms: 2.5 + x = -2.771023535 Solving 2.5 + x = -2.771023535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.771023535 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.771023535 + -2.5 x = -2.771023535 + -2.5 Combine like terms: -2.771023535 + -2.5 = -5.271023535 x = -5.271023535 Simplifying x = -5.271023535Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.271023535, -5.271023535}
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