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Simplifying 16x2 + 112x + 196 = 121(8x + -5) Reorder the terms: 196 + 112x + 16x2 = 121(8x + -5) Reorder the terms: 196 + 112x + 16x2 = 121(-5 + 8x) 196 + 112x + 16x2 = (-5 * 121 + 8x * 121) 196 + 112x + 16x2 = (-605 + 968x) Solving 196 + 112x + 16x2 = -605 + 968x Solving for variable 'x'. Reorder the terms: 196 + 605 + 112x + -968x + 16x2 = -605 + 968x + 605 + -968x Combine like terms: 196 + 605 = 801 801 + 112x + -968x + 16x2 = -605 + 968x + 605 + -968x Combine like terms: 112x + -968x = -856x 801 + -856x + 16x2 = -605 + 968x + 605 + -968x Reorder the terms: 801 + -856x + 16x2 = -605 + 605 + 968x + -968x Combine like terms: -605 + 605 = 0 801 + -856x + 16x2 = 0 + 968x + -968x 801 + -856x + 16x2 = 968x + -968x Combine like terms: 968x + -968x = 0 801 + -856x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 50.0625 + -53.5x + x2 = 0 Move the constant term to the right: Add '-50.0625' to each side of the equation. 50.0625 + -53.5x + -50.0625 + x2 = 0 + -50.0625 Reorder the terms: 50.0625 + -50.0625 + -53.5x + x2 = 0 + -50.0625 Combine like terms: 50.0625 + -50.0625 = 0.0000 0.0000 + -53.5x + x2 = 0 + -50.0625 -53.5x + x2 = 0 + -50.0625 Combine like terms: 0 + -50.0625 = -50.0625 -53.5x + x2 = -50.0625 The x term is -53.5x. Take half its coefficient (-26.75). Square it (715.5625) and add it to both sides. Add '715.5625' to each side of the equation. -53.5x + 715.5625 + x2 = -50.0625 + 715.5625 Reorder the terms: 715.5625 + -53.5x + x2 = -50.0625 + 715.5625 Combine like terms: -50.0625 + 715.5625 = 665.5 715.5625 + -53.5x + x2 = 665.5 Factor a perfect square on the left side: (x + -26.75)(x + -26.75) = 665.5 Calculate the square root of the right side: 25.797286679 Break this problem into two subproblems by setting (x + -26.75) equal to 25.797286679 and -25.797286679.Subproblem 1
x + -26.75 = 25.797286679 Simplifying x + -26.75 = 25.797286679 Reorder the terms: -26.75 + x = 25.797286679 Solving -26.75 + x = 25.797286679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.75' to each side of the equation. -26.75 + 26.75 + x = 25.797286679 + 26.75 Combine like terms: -26.75 + 26.75 = 0.00 0.00 + x = 25.797286679 + 26.75 x = 25.797286679 + 26.75 Combine like terms: 25.797286679 + 26.75 = 52.547286679 x = 52.547286679 Simplifying x = 52.547286679Subproblem 2
x + -26.75 = -25.797286679 Simplifying x + -26.75 = -25.797286679 Reorder the terms: -26.75 + x = -25.797286679 Solving -26.75 + x = -25.797286679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.75' to each side of the equation. -26.75 + 26.75 + x = -25.797286679 + 26.75 Combine like terms: -26.75 + 26.75 = 0.00 0.00 + x = -25.797286679 + 26.75 x = -25.797286679 + 26.75 Combine like terms: -25.797286679 + 26.75 = 0.952713321 x = 0.952713321 Simplifying x = 0.952713321Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.547286679, 0.952713321}
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