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Simplifying x2 + 6x + -40 = 9 Reorder the terms: -40 + 6x + x2 = 9 Solving -40 + 6x + x2 = 9 Solving for variable 'x'. Reorder the terms: -40 + -9 + 6x + x2 = 9 + -9 Combine like terms: -40 + -9 = -49 -49 + 6x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -49 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 6x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 6x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 6x + x2 = 0 + 49 6x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 6x + x2 = 49 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 49 + 9 Reorder the terms: 9 + 6x + x2 = 49 + 9 Combine like terms: 49 + 9 = 58 9 + 6x + x2 = 58 Factor a perfect square on the left side: (x + 3)(x + 3) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + 3) equal to 7.615773106 and -7.615773106.Subproblem 1
x + 3 = 7.615773106 Simplifying x + 3 = 7.615773106 Reorder the terms: 3 + x = 7.615773106 Solving 3 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.615773106 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.615773106 + -3 x = 7.615773106 + -3 Combine like terms: 7.615773106 + -3 = 4.615773106 x = 4.615773106 Simplifying x = 4.615773106Subproblem 2
x + 3 = -7.615773106 Simplifying x + 3 = -7.615773106 Reorder the terms: 3 + x = -7.615773106 Solving 3 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.615773106 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.615773106 + -3 x = -7.615773106 + -3 Combine like terms: -7.615773106 + -3 = -10.615773106 x = -10.615773106 Simplifying x = -10.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.615773106, -10.615773106}
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