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Simplifying 5x2 + -25x + -21 = 0 Reorder the terms: -21 + -25x + 5x2 = 0 Solving -21 + -25x + 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'. -4.2 + -5x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -5x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -5x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -5x + x2 = 0 + 4.2 -5x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -5x + x2 = 4.2 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 = 4.2 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 4.2 + 6.25 Combine like terms: 4.2 + 6.25 = 10.45 6.25 + -5x + x2 = 10.45 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 10.45 Calculate the square root of the right side: 3.232645975 Break this problem into two subproblems by setting (x + -2.5) equal to 3.232645975 and -3.232645975.Subproblem 1
x + -2.5 = 3.232645975 Simplifying x + -2.5 = 3.232645975 Reorder the terms: -2.5 + x = 3.232645975 Solving -2.5 + x = 3.232645975 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 = 3.232645975 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.232645975 + 2.5 x = 3.232645975 + 2.5 Combine like terms: 3.232645975 + 2.5 = 5.732645975 x = 5.732645975 Simplifying x = 5.732645975Subproblem 2
x + -2.5 = -3.232645975 Simplifying x + -2.5 = -3.232645975 Reorder the terms: -2.5 + x = -3.232645975 Solving -2.5 + x = -3.232645975 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 = -3.232645975 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.232645975 + 2.5 x = -3.232645975 + 2.5 Combine like terms: -3.232645975 + 2.5 = -0.732645975 x = -0.732645975 Simplifying x = -0.732645975Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.732645975, -0.732645975}
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