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Simplifying 8x(4x + -5) = 25 Reorder the terms: 8x(-5 + 4x) = 25 (-5 * 8x + 4x * 8x) = 25 (-40x + 32x2) = 25 Solving -40x + 32x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -40x + 32x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -40x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.78125 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.78125' to each side of the equation. -0.78125 + -1.25x + 0.78125 + x2 = 0 + 0.78125 Reorder the terms: -0.78125 + 0.78125 + -1.25x + x2 = 0 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + -1.25x + x2 = 0 + 0.78125 -1.25x + x2 = 0 + 0.78125 Combine like terms: 0 + 0.78125 = 0.78125 -1.25x + x2 = 0.78125 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 0.78125 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.78125 + 0.390625 Combine like terms: 0.78125 + 0.390625 = 1.171875 0.390625 + -1.25x + x2 = 1.171875 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 1.171875 Calculate the square root of the right side: 1.082531755 Break this problem into two subproblems by setting (x + -0.625) equal to 1.082531755 and -1.082531755.Subproblem 1
x + -0.625 = 1.082531755 Simplifying x + -0.625 = 1.082531755 Reorder the terms: -0.625 + x = 1.082531755 Solving -0.625 + x = 1.082531755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.082531755 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.082531755 + 0.625 x = 1.082531755 + 0.625 Combine like terms: 1.082531755 + 0.625 = 1.707531755 x = 1.707531755 Simplifying x = 1.707531755Subproblem 2
x + -0.625 = -1.082531755 Simplifying x + -0.625 = -1.082531755 Reorder the terms: -0.625 + x = -1.082531755 Solving -0.625 + x = -1.082531755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.082531755 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.082531755 + 0.625 x = -1.082531755 + 0.625 Combine like terms: -1.082531755 + 0.625 = -0.457531755 x = -0.457531755 Simplifying x = -0.457531755Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.707531755, -0.457531755}
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