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Simplifying 5x2 + -17x + 6 = 6x + -3 Reorder the terms: 6 + -17x + 5x2 = 6x + -3 Reorder the terms: 6 + -17x + 5x2 = -3 + 6x Solving 6 + -17x + 5x2 = -3 + 6x Solving for variable 'x'. Reorder the terms: 6 + 3 + -17x + -6x + 5x2 = -3 + 6x + 3 + -6x Combine like terms: 6 + 3 = 9 9 + -17x + -6x + 5x2 = -3 + 6x + 3 + -6x Combine like terms: -17x + -6x = -23x 9 + -23x + 5x2 = -3 + 6x + 3 + -6x Reorder the terms: 9 + -23x + 5x2 = -3 + 3 + 6x + -6x Combine like terms: -3 + 3 = 0 9 + -23x + 5x2 = 0 + 6x + -6x 9 + -23x + 5x2 = 6x + -6x Combine like terms: 6x + -6x = 0 9 + -23x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + -4.6x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -4.6x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -4.6x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -4.6x + x2 = 0 + -1.8 -4.6x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -4.6x + x2 = -1.8 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = -1.8 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = -1.8 + 5.29 Combine like terms: -1.8 + 5.29 = 3.49 5.29 + -4.6x + x2 = 3.49 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 3.49 Calculate the square root of the right side: 1.868154169 Break this problem into two subproblems by setting (x + -2.3) equal to 1.868154169 and -1.868154169.Subproblem 1
x + -2.3 = 1.868154169 Simplifying x + -2.3 = 1.868154169 Reorder the terms: -2.3 + x = 1.868154169 Solving -2.3 + x = 1.868154169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 1.868154169 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 1.868154169 + 2.3 x = 1.868154169 + 2.3 Combine like terms: 1.868154169 + 2.3 = 4.168154169 x = 4.168154169 Simplifying x = 4.168154169Subproblem 2
x + -2.3 = -1.868154169 Simplifying x + -2.3 = -1.868154169 Reorder the terms: -2.3 + x = -1.868154169 Solving -2.3 + x = -1.868154169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -1.868154169 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -1.868154169 + 2.3 x = -1.868154169 + 2.3 Combine like terms: -1.868154169 + 2.3 = 0.431845831 x = 0.431845831 Simplifying x = 0.431845831Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.168154169, 0.431845831}
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