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Simplifying -5x2 + 20x + -13 = 1 Reorder the terms: -13 + 20x + -5x2 = 1 Solving -13 + 20x + -5x2 = 1 Solving for variable 'x'. Reorder the terms: -13 + -1 + 20x + -5x2 = 1 + -1 Combine like terms: -13 + -1 = -14 -14 + 20x + -5x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -14 + 20x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 2.8 + -4x + x2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + -4x + -2.8 + x2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + -4x + x2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + -4x + x2 = 0 + -2.8 -4x + x2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 -4x + x2 = -2.8 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -2.8 + 4 Reorder the terms: 4 + -4x + x2 = -2.8 + 4 Combine like terms: -2.8 + 4 = 1.2 4 + -4x + x2 = 1.2 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (x + -2) equal to 1.095445115 and -1.095445115.Subproblem 1
x + -2 = 1.095445115 Simplifying x + -2 = 1.095445115 Reorder the terms: -2 + x = 1.095445115 Solving -2 + x = 1.095445115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.095445115 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.095445115 + 2 x = 1.095445115 + 2 Combine like terms: 1.095445115 + 2 = 3.095445115 x = 3.095445115 Simplifying x = 3.095445115Subproblem 2
x + -2 = -1.095445115 Simplifying x + -2 = -1.095445115 Reorder the terms: -2 + x = -1.095445115 Solving -2 + x = -1.095445115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.095445115 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.095445115 + 2 x = -1.095445115 + 2 Combine like terms: -1.095445115 + 2 = 0.904554885 x = 0.904554885 Simplifying x = 0.904554885Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.095445115, 0.904554885}
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