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Simplifying 14x + 12 = x2 + 2x Reorder the terms: 12 + 14x = x2 + 2x Reorder the terms: 12 + 14x = 2x + x2 Solving 12 + 14x = 2x + x2 Solving for variable 'x'. Combine like terms: 14x + -2x = 12x 12 + 12x + -1x2 = 2x + x2 + -2x + -1x2 Reorder the terms: 12 + 12x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 12 + 12x + -1x2 = 0 + x2 + -1x2 12 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + -12x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -12x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -12x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -12x + x2 = 0 + 12 -12x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -12x + x2 = 12 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 12 + 36 Reorder the terms: 36 + -12x + x2 = 12 + 36 Combine like terms: 12 + 36 = 48 36 + -12x + x2 = 48 Factor a perfect square on the left side: (x + -6)(x + -6) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + -6) equal to 6.92820323 and -6.92820323.Subproblem 1
x + -6 = 6.92820323 Simplifying x + -6 = 6.92820323 Reorder the terms: -6 + x = 6.92820323 Solving -6 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.92820323 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.92820323 + 6 x = 6.92820323 + 6 Combine like terms: 6.92820323 + 6 = 12.92820323 x = 12.92820323 Simplifying x = 12.92820323Subproblem 2
x + -6 = -6.92820323 Simplifying x + -6 = -6.92820323 Reorder the terms: -6 + x = -6.92820323 Solving -6 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.92820323 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.92820323 + 6 x = -6.92820323 + 6 Combine like terms: -6.92820323 + 6 = -0.92820323 x = -0.92820323 Simplifying x = -0.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.92820323, -0.92820323}
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