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Simplifying 5x2 + -17x + -9 = 12 Reorder the terms: -9 + -17x + 5x2 = 12 Solving -9 + -17x + 5x2 = 12 Solving for variable 'x'. Reorder the terms: -9 + -12 + -17x + 5x2 = 12 + -12 Combine like terms: -9 + -12 = -21 -21 + -17x + 5x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -21 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + -3.4x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -3.4x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -3.4x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -3.4x + x2 = 0 + 4.2 -3.4x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -3.4x + x2 = 4.2 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 = 4.2 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 4.2 + 2.89 Combine like terms: 4.2 + 2.89 = 7.09 2.89 + -3.4x + x2 = 7.09 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 7.09 Calculate the square root of the right side: 2.662705391 Break this problem into two subproblems by setting (x + -1.7) equal to 2.662705391 and -2.662705391.Subproblem 1
x + -1.7 = 2.662705391 Simplifying x + -1.7 = 2.662705391 Reorder the terms: -1.7 + x = 2.662705391 Solving -1.7 + x = 2.662705391 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 = 2.662705391 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 2.662705391 + 1.7 x = 2.662705391 + 1.7 Combine like terms: 2.662705391 + 1.7 = 4.362705391 x = 4.362705391 Simplifying x = 4.362705391Subproblem 2
x + -1.7 = -2.662705391 Simplifying x + -1.7 = -2.662705391 Reorder the terms: -1.7 + x = -2.662705391 Solving -1.7 + x = -2.662705391 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 = -2.662705391 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -2.662705391 + 1.7 x = -2.662705391 + 1.7 Combine like terms: -2.662705391 + 1.7 = -0.962705391 x = -0.962705391 Simplifying x = -0.962705391Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.362705391, -0.962705391}
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