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Simplifying 0 = -5x2 + -3x + 17 Reorder the terms: 0 = 17 + -3x + -5x2 Solving 0 = 17 + -3x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -17 = -17 -17 + 3x + 5x2 = 17 + -3x + -5x2 + -17 + 3x + 5x2 Reorder the terms: -17 + 3x + 5x2 = 17 + -17 + -3x + 3x + -5x2 + 5x2 Combine like terms: 17 + -17 = 0 -17 + 3x + 5x2 = 0 + -3x + 3x + -5x2 + 5x2 -17 + 3x + 5x2 = -3x + 3x + -5x2 + 5x2 Combine like terms: -3x + 3x = 0 -17 + 3x + 5x2 = 0 + -5x2 + 5x2 -17 + 3x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -17 + 3x + 5x2 = 0 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 = 1.568154169 x = 1.568154169 Simplifying x = 1.568154169Subproblem 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 = -2.168154169 x = -2.168154169 Simplifying x = -2.168154169Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.568154169, -2.168154169}
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