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Simplifying 5x2 + -112x + 256 = 0 Reorder the terms: 256 + -112x + 5x2 = 0 Solving 256 + -112x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 51.2 + -22.4x + x2 = 0 Move the constant term to the right: Add '-51.2' to each side of the equation. 51.2 + -22.4x + -51.2 + x2 = 0 + -51.2 Reorder the terms: 51.2 + -51.2 + -22.4x + x2 = 0 + -51.2 Combine like terms: 51.2 + -51.2 = 0.0 0.0 + -22.4x + x2 = 0 + -51.2 -22.4x + x2 = 0 + -51.2 Combine like terms: 0 + -51.2 = -51.2 -22.4x + x2 = -51.2 The x term is -22.4x. Take half its coefficient (-11.2). Square it (125.44) and add it to both sides. Add '125.44' to each side of the equation. -22.4x + 125.44 + x2 = -51.2 + 125.44 Reorder the terms: 125.44 + -22.4x + x2 = -51.2 + 125.44 Combine like terms: -51.2 + 125.44 = 74.24 125.44 + -22.4x + x2 = 74.24 Factor a perfect square on the left side: (x + -11.2)(x + -11.2) = 74.24 Calculate the square root of the right side: 8.616263691 Break this problem into two subproblems by setting (x + -11.2) equal to 8.616263691 and -8.616263691.Subproblem 1
x + -11.2 = 8.616263691 Simplifying x + -11.2 = 8.616263691 Reorder the terms: -11.2 + x = 8.616263691 Solving -11.2 + x = 8.616263691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.2' to each side of the equation. -11.2 + 11.2 + x = 8.616263691 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + x = 8.616263691 + 11.2 x = 8.616263691 + 11.2 Combine like terms: 8.616263691 + 11.2 = 19.816263691 x = 19.816263691 Simplifying x = 19.816263691Subproblem 2
x + -11.2 = -8.616263691 Simplifying x + -11.2 = -8.616263691 Reorder the terms: -11.2 + x = -8.616263691 Solving -11.2 + x = -8.616263691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.2' to each side of the equation. -11.2 + 11.2 + x = -8.616263691 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + x = -8.616263691 + 11.2 x = -8.616263691 + 11.2 Combine like terms: -8.616263691 + 11.2 = 2.583736309 x = 2.583736309 Simplifying x = 2.583736309Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.816263691, 2.583736309}
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