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Simplifying 8x2 + 25x + -20 = 0 Reorder the terms: -20 + 25x + 8x2 = 0 Solving -20 + 25x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.5 + 3.125x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 3.125x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 3.125x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 3.125x + x2 = 0 + 2.5 3.125x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 3.125x + x2 = 2.5 The x term is 3.125x. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125x + 2.44140625 + x2 = 2.5 + 2.44140625 Reorder the terms: 2.44140625 + 3.125x + x2 = 2.5 + 2.44140625 Combine like terms: 2.5 + 2.44140625 = 4.94140625 2.44140625 + 3.125x + x2 = 4.94140625 Factor a perfect square on the left side: (x + 1.5625)(x + 1.5625) = 4.94140625 Calculate the square root of the right side: 2.222927405 Break this problem into two subproblems by setting (x + 1.5625) equal to 2.222927405 and -2.222927405.Subproblem 1
x + 1.5625 = 2.222927405 Simplifying x + 1.5625 = 2.222927405 Reorder the terms: 1.5625 + x = 2.222927405 Solving 1.5625 + x = 2.222927405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = 2.222927405 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 2.222927405 + -1.5625 x = 2.222927405 + -1.5625 Combine like terms: 2.222927405 + -1.5625 = 0.660427405 x = 0.660427405 Simplifying x = 0.660427405Subproblem 2
x + 1.5625 = -2.222927405 Simplifying x + 1.5625 = -2.222927405 Reorder the terms: 1.5625 + x = -2.222927405 Solving 1.5625 + x = -2.222927405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = -2.222927405 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -2.222927405 + -1.5625 x = -2.222927405 + -1.5625 Combine like terms: -2.222927405 + -1.5625 = -3.785427405 x = -3.785427405 Simplifying x = -3.785427405Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.660427405, -3.785427405}
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