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Simplifying 5x2 + -5x + -21 = 0 Reorder the terms: -21 + -5x + 5x2 = 0 Solving -21 + -5x + 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 + -1x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -1x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -1x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -1x + x2 = 0 + 4.2 -1x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -1x + x2 = 4.2 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 4.2 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 4.2 + 0.25 Combine like terms: 4.2 + 0.25 = 4.45 0.25 + -1x + x2 = 4.45 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 4.45 Calculate the square root of the right side: 2.109502311 Break this problem into two subproblems by setting (x + -0.5) equal to 2.109502311 and -2.109502311.Subproblem 1
x + -0.5 = 2.109502311 Simplifying x + -0.5 = 2.109502311 Reorder the terms: -0.5 + x = 2.109502311 Solving -0.5 + x = 2.109502311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.109502311 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.109502311 + 0.5 x = 2.109502311 + 0.5 Combine like terms: 2.109502311 + 0.5 = 2.609502311 x = 2.609502311 Simplifying x = 2.609502311Subproblem 2
x + -0.5 = -2.109502311 Simplifying x + -0.5 = -2.109502311 Reorder the terms: -0.5 + x = -2.109502311 Solving -0.5 + x = -2.109502311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.109502311 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.109502311 + 0.5 x = -2.109502311 + 0.5 Combine like terms: -2.109502311 + 0.5 = -1.609502311 x = -1.609502311 Simplifying x = -1.609502311Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.609502311, -1.609502311}
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