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Simplifying 4x2 + -20x + -21 = 0 Reorder the terms: -21 + -20x + 4x2 = 0 Solving -21 + -20x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + -5x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -5x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -5x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -5x + x2 = 0 + 5.25 -5x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -5x + x2 = 5.25 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 5.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 5.25 + 6.25 Combine like terms: 5.25 + 6.25 = 11.5 6.25 + -5x + x2 = 11.5 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + -2.5) equal to 3.391164992 and -3.391164992.Subproblem 1
x + -2.5 = 3.391164992 Simplifying x + -2.5 = 3.391164992 Reorder the terms: -2.5 + x = 3.391164992 Solving -2.5 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.391164992 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.391164992 + 2.5 x = 3.391164992 + 2.5 Combine like terms: 3.391164992 + 2.5 = 5.891164992 x = 5.891164992 Simplifying x = 5.891164992Subproblem 2
x + -2.5 = -3.391164992 Simplifying x + -2.5 = -3.391164992 Reorder the terms: -2.5 + x = -3.391164992 Solving -2.5 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.391164992 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.391164992 + 2.5 x = -3.391164992 + 2.5 Combine like terms: -3.391164992 + 2.5 = -0.891164992 x = -0.891164992 Simplifying x = -0.891164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.891164992, -0.891164992}
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