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Simplifying 5x2 + -20x + -6 = 0 Reorder the terms: -6 + -20x + 5x2 = 0 Solving -6 + -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'. -1.2 + -4x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -4x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -4x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -4x + x2 = 0 + 1.2 -4x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -4x + x2 = 1.2 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 = 1.2 + 4 Reorder the terms: 4 + -4x + x2 = 1.2 + 4 Combine like terms: 1.2 + 4 = 5.2 4 + -4x + x2 = 5.2 Factor a perfect square on the left side: (x + -2)(x + -2) = 5.2 Calculate the square root of the right side: 2.28035085 Break this problem into two subproblems by setting (x + -2) equal to 2.28035085 and -2.28035085.Subproblem 1
x + -2 = 2.28035085 Simplifying x + -2 = 2.28035085 Reorder the terms: -2 + x = 2.28035085 Solving -2 + x = 2.28035085 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 = 2.28035085 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.28035085 + 2 x = 2.28035085 + 2 Combine like terms: 2.28035085 + 2 = 4.28035085 x = 4.28035085 Simplifying x = 4.28035085Subproblem 2
x + -2 = -2.28035085 Simplifying x + -2 = -2.28035085 Reorder the terms: -2 + x = -2.28035085 Solving -2 + x = -2.28035085 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 = -2.28035085 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.28035085 + 2 x = -2.28035085 + 2 Combine like terms: -2.28035085 + 2 = -0.28035085 x = -0.28035085 Simplifying x = -0.28035085Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.28035085, -0.28035085}
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