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Simplifying 5x2 = 13x + 17 Reorder the terms: 5x2 = 17 + 13x Solving 5x2 = 17 + 13x Solving for variable 'x'. Reorder the terms: -17 + -13x + 5x2 = 17 + 13x + -17 + -13x Reorder the terms: -17 + -13x + 5x2 = 17 + -17 + 13x + -13x Combine like terms: 17 + -17 = 0 -17 + -13x + 5x2 = 0 + 13x + -13x -17 + -13x + 5x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -17 + -13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + -2.6x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + -2.6x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + -2.6x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + -2.6x + x2 = 0 + 3.4 -2.6x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 -2.6x + x2 = 3.4 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = 3.4 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = 3.4 + 1.69 Combine like terms: 3.4 + 1.69 = 5.09 1.69 + -2.6x + x2 = 5.09 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 5.09 Calculate the square root of the right side: 2.256102835 Break this problem into two subproblems by setting (x + -1.3) equal to 2.256102835 and -2.256102835.Subproblem 1
x + -1.3 = 2.256102835 Simplifying x + -1.3 = 2.256102835 Reorder the terms: -1.3 + x = 2.256102835 Solving -1.3 + x = 2.256102835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 2.256102835 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 2.256102835 + 1.3 x = 2.256102835 + 1.3 Combine like terms: 2.256102835 + 1.3 = 3.556102835 x = 3.556102835 Simplifying x = 3.556102835Subproblem 2
x + -1.3 = -2.256102835 Simplifying x + -1.3 = -2.256102835 Reorder the terms: -1.3 + x = -2.256102835 Solving -1.3 + x = -2.256102835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = -2.256102835 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -2.256102835 + 1.3 x = -2.256102835 + 1.3 Combine like terms: -2.256102835 + 1.3 = -0.956102835 x = -0.956102835 Simplifying x = -0.956102835Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.556102835, -0.956102835}
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