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Simplifying 0 = 5x2 + -13x + -5 Reorder the terms: 0 = -5 + -13x + 5x2 Solving 0 = -5 + -13x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + 13x + -5x2 = -5 + -13x + 5x2 + 5 + 13x + -5x2 Reorder the terms: 5 + 13x + -5x2 = -5 + 5 + -13x + 13x + 5x2 + -5x2 Combine like terms: -5 + 5 = 0 5 + 13x + -5x2 = 0 + -13x + 13x + 5x2 + -5x2 5 + 13x + -5x2 = -13x + 13x + 5x2 + -5x2 Combine like terms: -13x + 13x = 0 5 + 13x + -5x2 = 0 + 5x2 + -5x2 5 + 13x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 5 + 13x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1 + -2.6x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.6x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.6x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.6x + x2 = 0 + 1 -2.6x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.6x + x2 = 1 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 = 1 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = 1 + 1.69 Combine like terms: 1 + 1.69 = 2.69 1.69 + -2.6x + x2 = 2.69 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 2.69 Calculate the square root of the right side: 1.640121947 Break this problem into two subproblems by setting (x + -1.3) equal to 1.640121947 and -1.640121947.Subproblem 1
x + -1.3 = 1.640121947 Simplifying x + -1.3 = 1.640121947 Reorder the terms: -1.3 + x = 1.640121947 Solving -1.3 + x = 1.640121947 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 = 1.640121947 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 1.640121947 + 1.3 x = 1.640121947 + 1.3 Combine like terms: 1.640121947 + 1.3 = 2.940121947 x = 2.940121947 Simplifying x = 2.940121947Subproblem 2
x + -1.3 = -1.640121947 Simplifying x + -1.3 = -1.640121947 Reorder the terms: -1.3 + x = -1.640121947 Solving -1.3 + x = -1.640121947 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 = -1.640121947 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -1.640121947 + 1.3 x = -1.640121947 + 1.3 Combine like terms: -1.640121947 + 1.3 = -0.340121947 x = -0.340121947 Simplifying x = -0.340121947Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.940121947, -0.340121947}
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