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Simplifying 4x + -7x(x + -9) = 42 Reorder the terms: 4x + -7x(-9 + x) = 42 4x + (-9 * -7x + x * -7x) = 42 4x + (63x + -7x2) = 42 Combine like terms: 4x + 63x = 67x 67x + -7x2 = 42 Solving 67x + -7x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 67x + -7x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 67x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 6 + -9.571428571x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -9.571428571x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -9.571428571x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9.571428571x + x2 = 0 + -6 -9.571428571x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -9.571428571x + x2 = -6 The x term is -9.571428571x. Take half its coefficient (-4.785714286). Square it (22.90306123) and add it to both sides. Add '22.90306123' to each side of the equation. -9.571428571x + 22.90306123 + x2 = -6 + 22.90306123 Reorder the terms: 22.90306123 + -9.571428571x + x2 = -6 + 22.90306123 Combine like terms: -6 + 22.90306123 = 16.90306123 22.90306123 + -9.571428571x + x2 = 16.90306123 Factor a perfect square on the left side: (x + -4.785714286)(x + -4.785714286) = 16.90306123 Calculate the square root of the right side: 4.111333267 Break this problem into two subproblems by setting (x + -4.785714286) equal to 4.111333267 and -4.111333267.Subproblem 1
x + -4.785714286 = 4.111333267 Simplifying x + -4.785714286 = 4.111333267 Reorder the terms: -4.785714286 + x = 4.111333267 Solving -4.785714286 + x = 4.111333267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.785714286' to each side of the equation. -4.785714286 + 4.785714286 + x = 4.111333267 + 4.785714286 Combine like terms: -4.785714286 + 4.785714286 = 0.000000000 0.000000000 + x = 4.111333267 + 4.785714286 x = 4.111333267 + 4.785714286 Combine like terms: 4.111333267 + 4.785714286 = 8.897047553 x = 8.897047553 Simplifying x = 8.897047553Subproblem 2
x + -4.785714286 = -4.111333267 Simplifying x + -4.785714286 = -4.111333267 Reorder the terms: -4.785714286 + x = -4.111333267 Solving -4.785714286 + x = -4.111333267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.785714286' to each side of the equation. -4.785714286 + 4.785714286 + x = -4.111333267 + 4.785714286 Combine like terms: -4.785714286 + 4.785714286 = 0.000000000 0.000000000 + x = -4.111333267 + 4.785714286 x = -4.111333267 + 4.785714286 Combine like terms: -4.111333267 + 4.785714286 = 0.674381019 x = 0.674381019 Simplifying x = 0.674381019Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.897047553, 0.674381019}
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