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Simplifying 2x(-4x + 20) = 25 Reorder the terms: 2x(20 + -4x) = 25 (20 * 2x + -4x * 2x) = 25 (40x + -8x2) = 25 Solving 40x + -8x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 40x + -8x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 40x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 3.125 + -5x + x2 = 0 Move the constant term to the right: Add '-3.125' to each side of the equation. 3.125 + -5x + -3.125 + x2 = 0 + -3.125 Reorder the terms: 3.125 + -3.125 + -5x + x2 = 0 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + -5x + x2 = 0 + -3.125 -5x + x2 = 0 + -3.125 Combine like terms: 0 + -3.125 = -3.125 -5x + x2 = -3.125 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 = -3.125 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -3.125 + 6.25 Combine like terms: -3.125 + 6.25 = 3.125 6.25 + -5x + x2 = 3.125 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (x + -2.5) equal to 1.767766953 and -1.767766953.Subproblem 1
x + -2.5 = 1.767766953 Simplifying x + -2.5 = 1.767766953 Reorder the terms: -2.5 + x = 1.767766953 Solving -2.5 + x = 1.767766953 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 = 1.767766953 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.767766953 + 2.5 x = 1.767766953 + 2.5 Combine like terms: 1.767766953 + 2.5 = 4.267766953 x = 4.267766953 Simplifying x = 4.267766953Subproblem 2
x + -2.5 = -1.767766953 Simplifying x + -2.5 = -1.767766953 Reorder the terms: -2.5 + x = -1.767766953 Solving -2.5 + x = -1.767766953 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 = -1.767766953 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.767766953 + 2.5 x = -1.767766953 + 2.5 Combine like terms: -1.767766953 + 2.5 = 0.732233047 x = 0.732233047 Simplifying x = 0.732233047Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.267766953, 0.732233047}
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