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Simplifying x2 + 30x + 70 = 6 Reorder the terms: 70 + 30x + x2 = 6 Solving 70 + 30x + x2 = 6 Solving for variable 'x'. Reorder the terms: 70 + -6 + 30x + x2 = 6 + -6 Combine like terms: 70 + -6 = 64 64 + 30x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 64 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + 30x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + 30x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 30x + x2 = 0 + -64 30x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 30x + x2 = -64 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -64 + 225 Reorder the terms: 225 + 30x + x2 = -64 + 225 Combine like terms: -64 + 225 = 161 225 + 30x + x2 = 161 Factor a perfect square on the left side: (x + 15)(x + 15) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (x + 15) equal to 12.68857754 and -12.68857754.Subproblem 1
x + 15 = 12.68857754 Simplifying x + 15 = 12.68857754 Reorder the terms: 15 + x = 12.68857754 Solving 15 + x = 12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 12.68857754 + -15 Combine like terms: 15 + -15 = 0 0 + x = 12.68857754 + -15 x = 12.68857754 + -15 Combine like terms: 12.68857754 + -15 = -2.31142246 x = -2.31142246 Simplifying x = -2.31142246Subproblem 2
x + 15 = -12.68857754 Simplifying x + 15 = -12.68857754 Reorder the terms: 15 + x = -12.68857754 Solving 15 + x = -12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -12.68857754 + -15 Combine like terms: 15 + -15 = 0 0 + x = -12.68857754 + -15 x = -12.68857754 + -15 Combine like terms: -12.68857754 + -15 = -27.68857754 x = -27.68857754 Simplifying x = -27.68857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.31142246, -27.68857754}
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