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Simplifying (2x + -7)(x + -7) = 16 Reorder the terms: (-7 + 2x)(x + -7) = 16 Reorder the terms: (-7 + 2x)(-7 + x) = 16 Multiply (-7 + 2x) * (-7 + x) (-7(-7 + x) + 2x * (-7 + x)) = 16 ((-7 * -7 + x * -7) + 2x * (-7 + x)) = 16 ((49 + -7x) + 2x * (-7 + x)) = 16 (49 + -7x + (-7 * 2x + x * 2x)) = 16 (49 + -7x + (-14x + 2x2)) = 16 Combine like terms: -7x + -14x = -21x (49 + -21x + 2x2) = 16 Solving 49 + -21x + 2x2 = 16 Solving for variable 'x'. Reorder the terms: 49 + -16 + -21x + 2x2 = 16 + -16 Combine like terms: 49 + -16 = 33 33 + -21x + 2x2 = 16 + -16 Combine like terms: 16 + -16 = 0 33 + -21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 16.5 + -10.5x + x2 = 0 Move the constant term to the right: Add '-16.5' to each side of the equation. 16.5 + -10.5x + -16.5 + x2 = 0 + -16.5 Reorder the terms: 16.5 + -16.5 + -10.5x + x2 = 0 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + -10.5x + x2 = 0 + -16.5 -10.5x + x2 = 0 + -16.5 Combine like terms: 0 + -16.5 = -16.5 -10.5x + x2 = -16.5 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = -16.5 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -16.5 + 27.5625 Combine like terms: -16.5 + 27.5625 = 11.0625 27.5625 + -10.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + -5.25) equal to 3.326033674 and -3.326033674.Subproblem 1
x + -5.25 = 3.326033674 Simplifying x + -5.25 = 3.326033674 Reorder the terms: -5.25 + x = 3.326033674 Solving -5.25 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 3.326033674 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 3.326033674 + 5.25 x = 3.326033674 + 5.25 Combine like terms: 3.326033674 + 5.25 = 8.576033674 x = 8.576033674 Simplifying x = 8.576033674Subproblem 2
x + -5.25 = -3.326033674 Simplifying x + -5.25 = -3.326033674 Reorder the terms: -5.25 + x = -3.326033674 Solving -5.25 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -3.326033674 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -3.326033674 + 5.25 x = -3.326033674 + 5.25 Combine like terms: -3.326033674 + 5.25 = 1.923966326 x = 1.923966326 Simplifying x = 1.923966326Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.576033674, 1.923966326}
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