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Simplifying 5x2 + -17x + -64 = 0 Reorder the terms: -64 + -17x + 5x2 = 0 Solving -64 + -17x + 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'. -12.8 + -3.4x + x2 = 0 Move the constant term to the right: Add '12.8' to each side of the equation. -12.8 + -3.4x + 12.8 + x2 = 0 + 12.8 Reorder the terms: -12.8 + 12.8 + -3.4x + x2 = 0 + 12.8 Combine like terms: -12.8 + 12.8 = 0.0 0.0 + -3.4x + x2 = 0 + 12.8 -3.4x + x2 = 0 + 12.8 Combine like terms: 0 + 12.8 = 12.8 -3.4x + x2 = 12.8 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 12.8 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 12.8 + 2.89 Combine like terms: 12.8 + 2.89 = 15.69 2.89 + -3.4x + x2 = 15.69 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 15.69 Calculate the square root of the right side: 3.961060464 Break this problem into two subproblems by setting (x + -1.7) equal to 3.961060464 and -3.961060464.Subproblem 1
x + -1.7 = 3.961060464 Simplifying x + -1.7 = 3.961060464 Reorder the terms: -1.7 + x = 3.961060464 Solving -1.7 + x = 3.961060464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 3.961060464 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 3.961060464 + 1.7 x = 3.961060464 + 1.7 Combine like terms: 3.961060464 + 1.7 = 5.661060464 x = 5.661060464 Simplifying x = 5.661060464Subproblem 2
x + -1.7 = -3.961060464 Simplifying x + -1.7 = -3.961060464 Reorder the terms: -1.7 + x = -3.961060464 Solving -1.7 + x = -3.961060464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -3.961060464 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -3.961060464 + 1.7 x = -3.961060464 + 1.7 Combine like terms: -3.961060464 + 1.7 = -2.261060464 x = -2.261060464 Simplifying x = -2.261060464Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.661060464, -2.261060464}
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