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Simplifying 4x2 + -1x = 20 Reorder the terms: -1x + 4x2 = 20 Solving -1x + 4x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -1x + 4x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5 + -0.25x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.25x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.25x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.25x + x2 = 0 + 5 -0.25x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.25x + x2 = 5 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 5 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 5 + 0.015625 Combine like terms: 5 + 0.015625 = 5.015625 0.015625 + -0.25x + x2 = 5.015625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 5.015625 Calculate the square root of the right side: 2.239559108 Break this problem into two subproblems by setting (x + -0.125) equal to 2.239559108 and -2.239559108.Subproblem 1
x + -0.125 = 2.239559108 Simplifying x + -0.125 = 2.239559108 Reorder the terms: -0.125 + x = 2.239559108 Solving -0.125 + x = 2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 2.239559108 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 2.239559108 + 0.125 x = 2.239559108 + 0.125 Combine like terms: 2.239559108 + 0.125 = 2.364559108 x = 2.364559108 Simplifying x = 2.364559108Subproblem 2
x + -0.125 = -2.239559108 Simplifying x + -0.125 = -2.239559108 Reorder the terms: -0.125 + x = -2.239559108 Solving -0.125 + x = -2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -2.239559108 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -2.239559108 + 0.125 x = -2.239559108 + 0.125 Combine like terms: -2.239559108 + 0.125 = -2.114559108 x = -2.114559108 Simplifying x = -2.114559108Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.364559108, -2.114559108}
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