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Simplifying 6x2 + 12x + -94 = -5 Reorder the terms: -94 + 12x + 6x2 = -5 Solving -94 + 12x + 6x2 = -5 Solving for variable 'x'. Reorder the terms: -94 + 5 + 12x + 6x2 = -5 + 5 Combine like terms: -94 + 5 = -89 -89 + 12x + 6x2 = -5 + 5 Combine like terms: -5 + 5 = 0 -89 + 12x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -14.83333333 + 2x + x2 = 0 Move the constant term to the right: Add '14.83333333' to each side of the equation. -14.83333333 + 2x + 14.83333333 + x2 = 0 + 14.83333333 Reorder the terms: -14.83333333 + 14.83333333 + 2x + x2 = 0 + 14.83333333 Combine like terms: -14.83333333 + 14.83333333 = 0.00000000 0.00000000 + 2x + x2 = 0 + 14.83333333 2x + x2 = 0 + 14.83333333 Combine like terms: 0 + 14.83333333 = 14.83333333 2x + x2 = 14.83333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 14.83333333 + 1 Reorder the terms: 1 + 2x + x2 = 14.83333333 + 1 Combine like terms: 14.83333333 + 1 = 15.83333333 1 + 2x + x2 = 15.83333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 15.83333333 Calculate the square root of the right side: 3.979112128 Break this problem into two subproblems by setting (x + 1) equal to 3.979112128 and -3.979112128.Subproblem 1
x + 1 = 3.979112128 Simplifying x + 1 = 3.979112128 Reorder the terms: 1 + x = 3.979112128 Solving 1 + x = 3.979112128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.979112128 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.979112128 + -1 x = 3.979112128 + -1 Combine like terms: 3.979112128 + -1 = 2.979112128 x = 2.979112128 Simplifying x = 2.979112128Subproblem 2
x + 1 = -3.979112128 Simplifying x + 1 = -3.979112128 Reorder the terms: 1 + x = -3.979112128 Solving 1 + x = -3.979112128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.979112128 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.979112128 + -1 x = -3.979112128 + -1 Combine like terms: -3.979112128 + -1 = -4.979112128 x = -4.979112128 Simplifying x = -4.979112128Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.979112128, -4.979112128}
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