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Simplifying -5x2 + -20x + 13 = 0 Reorder the terms: 13 + -20x + -5x2 = 0 Solving 13 + -20x + -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'. -2.6 + 4x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 4x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 4x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 4x + x2 = 0 + 2.6 4x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 4x + x2 = 2.6 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 = 2.6 + 4 Reorder the terms: 4 + 4x + x2 = 2.6 + 4 Combine like terms: 2.6 + 4 = 6.6 4 + 4x + x2 = 6.6 Factor a perfect square on the left side: (x + 2)(x + 2) = 6.6 Calculate the square root of the right side: 2.569046516 Break this problem into two subproblems by setting (x + 2) equal to 2.569046516 and -2.569046516.Subproblem 1
x + 2 = 2.569046516 Simplifying x + 2 = 2.569046516 Reorder the terms: 2 + x = 2.569046516 Solving 2 + x = 2.569046516 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 = 2.569046516 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.569046516 + -2 x = 2.569046516 + -2 Combine like terms: 2.569046516 + -2 = 0.569046516 x = 0.569046516 Simplifying x = 0.569046516Subproblem 2
x + 2 = -2.569046516 Simplifying x + 2 = -2.569046516 Reorder the terms: 2 + x = -2.569046516 Solving 2 + x = -2.569046516 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 = -2.569046516 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.569046516 + -2 x = -2.569046516 + -2 Combine like terms: -2.569046516 + -2 = -4.569046516 x = -4.569046516 Simplifying x = -4.569046516Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.569046516, -4.569046516}
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