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Simplifying 2x + 14 = x2 + -10x + -25 Reorder the terms: 14 + 2x = x2 + -10x + -25 Reorder the terms: 14 + 2x = -25 + -10x + x2 Solving 14 + 2x = -25 + -10x + x2 Solving for variable 'x'. Reorder the terms: 14 + 25 + 2x + 10x + -1x2 = -25 + -10x + x2 + 25 + 10x + -1x2 Combine like terms: 14 + 25 = 39 39 + 2x + 10x + -1x2 = -25 + -10x + x2 + 25 + 10x + -1x2 Combine like terms: 2x + 10x = 12x 39 + 12x + -1x2 = -25 + -10x + x2 + 25 + 10x + -1x2 Reorder the terms: 39 + 12x + -1x2 = -25 + 25 + -10x + 10x + x2 + -1x2 Combine like terms: -25 + 25 = 0 39 + 12x + -1x2 = 0 + -10x + 10x + x2 + -1x2 39 + 12x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 39 + 12x + -1x2 = 0 + x2 + -1x2 39 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 39 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -39 + -12x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + -12x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -12x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -12x + x2 = 0 + 39 -12x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -12x + x2 = 39 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 = 39 + 36 Reorder the terms: 36 + -12x + x2 = 39 + 36 Combine like terms: 39 + 36 = 75 36 + -12x + x2 = 75 Factor a perfect square on the left side: (x + -6)(x + -6) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -6) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -6 = 8.660254038 Simplifying x + -6 = 8.660254038 Reorder the terms: -6 + x = 8.660254038 Solving -6 + x = 8.660254038 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 = 8.660254038 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.660254038 + 6 x = 8.660254038 + 6 Combine like terms: 8.660254038 + 6 = 14.660254038 x = 14.660254038 Simplifying x = 14.660254038Subproblem 2
x + -6 = -8.660254038 Simplifying x + -6 = -8.660254038 Reorder the terms: -6 + x = -8.660254038 Solving -6 + x = -8.660254038 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 = -8.660254038 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.660254038 + 6 x = -8.660254038 + 6 Combine like terms: -8.660254038 + 6 = -2.660254038 x = -2.660254038 Simplifying x = -2.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.660254038, -2.660254038}
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