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Simplifying 5x2 + -20x = 28 Reorder the terms: -20x + 5x2 = 28 Solving -20x + 5x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + -20x + 5x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + -4x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -4x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -4x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -4x + x2 = 0 + 5.6 -4x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -4x + x2 = 5.6 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 = 5.6 + 4 Reorder the terms: 4 + -4x + x2 = 5.6 + 4 Combine like terms: 5.6 + 4 = 9.6 4 + -4x + x2 = 9.6 Factor a perfect square on the left side: (x + -2)(x + -2) = 9.6 Calculate the square root of the right side: 3.098386677 Break this problem into two subproblems by setting (x + -2) equal to 3.098386677 and -3.098386677.Subproblem 1
x + -2 = 3.098386677 Simplifying x + -2 = 3.098386677 Reorder the terms: -2 + x = 3.098386677 Solving -2 + x = 3.098386677 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 = 3.098386677 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.098386677 + 2 x = 3.098386677 + 2 Combine like terms: 3.098386677 + 2 = 5.098386677 x = 5.098386677 Simplifying x = 5.098386677Subproblem 2
x + -2 = -3.098386677 Simplifying x + -2 = -3.098386677 Reorder the terms: -2 + x = -3.098386677 Solving -2 + x = -3.098386677 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 = -3.098386677 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.098386677 + 2 x = -3.098386677 + 2 Combine like terms: -3.098386677 + 2 = -1.098386677 x = -1.098386677 Simplifying x = -1.098386677Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.098386677, -1.098386677}
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