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Simplifying 12x2 + -12x = 7 Reorder the terms: -12x + 12x2 = 7 Solving -12x + 12x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -12x + 12x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -12x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.5833333333 + -1x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + -1x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + -1x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.5833333333 -1x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 -1x + x2 = 0.5833333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.5833333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.5833333333 + 0.25 Combine like terms: 0.5833333333 + 0.25 = 0.8333333333 0.25 + -1x + x2 = 0.8333333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.8333333333 Calculate the square root of the right side: 0.912870929 Break this problem into two subproblems by setting (x + -0.5) equal to 0.912870929 and -0.912870929.Subproblem 1
x + -0.5 = 0.912870929 Simplifying x + -0.5 = 0.912870929 Reorder the terms: -0.5 + x = 0.912870929 Solving -0.5 + x = 0.912870929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.912870929 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.912870929 + 0.5 x = 0.912870929 + 0.5 Combine like terms: 0.912870929 + 0.5 = 1.412870929 x = 1.412870929 Simplifying x = 1.412870929Subproblem 2
x + -0.5 = -0.912870929 Simplifying x + -0.5 = -0.912870929 Reorder the terms: -0.5 + x = -0.912870929 Solving -0.5 + x = -0.912870929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.912870929 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.912870929 + 0.5 x = -0.912870929 + 0.5 Combine like terms: -0.912870929 + 0.5 = -0.412870929 x = -0.412870929 Simplifying x = -0.412870929Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.412870929, -0.412870929}
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