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Simplifying 5x2 + -3x + -17 = 0 Reorder the terms: -17 + -3x + 5x2 = 0 Solving -17 + -3x + 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'. -3.4 + -0.6x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + -0.6x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + -0.6x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + -0.6x + x2 = 0 + 3.4 -0.6x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 -0.6x + x2 = 3.4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 3.4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 3.4 + 0.09 Combine like terms: 3.4 + 0.09 = 3.49 0.09 + -0.6x + x2 = 3.49 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 3.49 Calculate the square root of the right side: 1.868154169 Break this problem into two subproblems by setting (x + -0.3) equal to 1.868154169 and -1.868154169.Subproblem 1
x + -0.3 = 1.868154169 Simplifying x + -0.3 = 1.868154169 Reorder the terms: -0.3 + x = 1.868154169 Solving -0.3 + x = 1.868154169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.868154169 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.868154169 + 0.3 x = 1.868154169 + 0.3 Combine like terms: 1.868154169 + 0.3 = 2.168154169 x = 2.168154169 Simplifying x = 2.168154169Subproblem 2
x + -0.3 = -1.868154169 Simplifying x + -0.3 = -1.868154169 Reorder the terms: -0.3 + x = -1.868154169 Solving -0.3 + x = -1.868154169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.868154169 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.868154169 + 0.3 x = -1.868154169 + 0.3 Combine like terms: -1.868154169 + 0.3 = -1.568154169 x = -1.568154169 Simplifying x = -1.568154169Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.168154169, -1.568154169}
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