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Simplifying x2 + -16 = 2x2 + -14x + 21 Reorder the terms: -16 + x2 = 2x2 + -14x + 21 Reorder the terms: -16 + x2 = 21 + -14x + 2x2 Solving -16 + x2 = 21 + -14x + 2x2 Solving for variable 'x'. Reorder the terms: -16 + -21 + 14x + x2 + -2x2 = 21 + -14x + 2x2 + -21 + 14x + -2x2 Combine like terms: -16 + -21 = -37 -37 + 14x + x2 + -2x2 = 21 + -14x + 2x2 + -21 + 14x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -37 + 14x + -1x2 = 21 + -14x + 2x2 + -21 + 14x + -2x2 Reorder the terms: -37 + 14x + -1x2 = 21 + -21 + -14x + 14x + 2x2 + -2x2 Combine like terms: 21 + -21 = 0 -37 + 14x + -1x2 = 0 + -14x + 14x + 2x2 + -2x2 -37 + 14x + -1x2 = -14x + 14x + 2x2 + -2x2 Combine like terms: -14x + 14x = 0 -37 + 14x + -1x2 = 0 + 2x2 + -2x2 -37 + 14x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -37 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 37 + -14x + x2 = 0 Move the constant term to the right: Add '-37' to each side of the equation. 37 + -14x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + -14x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -14x + x2 = 0 + -37 -14x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 -14x + x2 = -37 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -37 + 49 Reorder the terms: 49 + -14x + x2 = -37 + 49 Combine like terms: -37 + 49 = 12 49 + -14x + x2 = 12 Factor a perfect square on the left side: (x + -7)(x + -7) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -7) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -7 = 3.464101615 Simplifying x + -7 = 3.464101615 Reorder the terms: -7 + x = 3.464101615 Solving -7 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 3.464101615 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.464101615 + 7 x = 3.464101615 + 7 Combine like terms: 3.464101615 + 7 = 10.464101615 x = 10.464101615 Simplifying x = 10.464101615Subproblem 2
x + -7 = -3.464101615 Simplifying x + -7 = -3.464101615 Reorder the terms: -7 + x = -3.464101615 Solving -7 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -3.464101615 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.464101615 + 7 x = -3.464101615 + 7 Combine like terms: -3.464101615 + 7 = 3.535898385 x = 3.535898385 Simplifying x = 3.535898385Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.464101615, 3.535898385}
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