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Simplifying 0 = 2.5x2 + -17x + -10 Reorder the terms: 0 = -10 + -17x + 2.5x2 Solving 0 = -10 + -17x + 2.5x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + 17x + -2.5x2 = -10 + -17x + 2.5x2 + 10 + 17x + -2.5x2 Reorder the terms: 10 + 17x + -2.5x2 = -10 + 10 + -17x + 17x + 2.5x2 + -2.5x2 Combine like terms: -10 + 10 = 0 10 + 17x + -2.5x2 = 0 + -17x + 17x + 2.5x2 + -2.5x2 10 + 17x + -2.5x2 = -17x + 17x + 2.5x2 + -2.5x2 Combine like terms: -17x + 17x = 0 10 + 17x + -2.5x2 = 0 + 2.5x2 + -2.5x2 10 + 17x + -2.5x2 = 2.5x2 + -2.5x2 Combine like terms: 2.5x2 + -2.5x2 = 0.0 10 + 17x + -2.5x2 = 0.0 Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. -4 + -6.8x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -6.8x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -6.8x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6.8x + x2 = 0 + 4 -6.8x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6.8x + x2 = 4 The x term is -6.8x. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8x + 11.56 + x2 = 4 + 11.56 Reorder the terms: 11.56 + -6.8x + x2 = 4 + 11.56 Combine like terms: 4 + 11.56 = 15.56 11.56 + -6.8x + x2 = 15.56 Factor a perfect square on the left side: (x + -3.4)(x + -3.4) = 15.56 Calculate the square root of the right side: 3.944616585 Break this problem into two subproblems by setting (x + -3.4) equal to 3.944616585 and -3.944616585.Subproblem 1
x + -3.4 = 3.944616585 Simplifying x + -3.4 = 3.944616585 Reorder the terms: -3.4 + x = 3.944616585 Solving -3.4 + x = 3.944616585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = 3.944616585 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = 3.944616585 + 3.4 x = 3.944616585 + 3.4 Combine like terms: 3.944616585 + 3.4 = 7.344616585 x = 7.344616585 Simplifying x = 7.344616585Subproblem 2
x + -3.4 = -3.944616585 Simplifying x + -3.4 = -3.944616585 Reorder the terms: -3.4 + x = -3.944616585 Solving -3.4 + x = -3.944616585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = -3.944616585 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = -3.944616585 + 3.4 x = -3.944616585 + 3.4 Combine like terms: -3.944616585 + 3.4 = -0.544616585 x = -0.544616585 Simplifying x = -0.544616585Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.344616585, -0.544616585}
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