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Simplifying 8x(5x + -4) = 5 Reorder the terms: 8x(-4 + 5x) = 5 (-4 * 8x + 5x * 8x) = 5 (-32x + 40x2) = 5 Solving -32x + 40x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -32x + 40x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -32x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.125 + -0.8x + x2 = 0.0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.8x + 0.125 + x2 = 0.0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.8x + x2 = 0.0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.8x + x2 = 0.0 + 0.125 -0.8x + x2 = 0.0 + 0.125 Combine like terms: 0.0 + 0.125 = 0.125 -0.8x + x2 = 0.125 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 0.125 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.125 + 0.16 Combine like terms: 0.125 + 0.16 = 0.285 0.16 + -0.8x + x2 = 0.285 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.285 Calculate the square root of the right side: 0.533853913 Break this problem into two subproblems by setting (x + -0.4) equal to 0.533853913 and -0.533853913.Subproblem 1
x + -0.4 = 0.533853913 Simplifying x + -0.4 = 0.533853913 Reorder the terms: -0.4 + x = 0.533853913 Solving -0.4 + x = 0.533853913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.533853913 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.533853913 + 0.4 x = 0.533853913 + 0.4 Combine like terms: 0.533853913 + 0.4 = 0.933853913 x = 0.933853913 Simplifying x = 0.933853913Subproblem 2
x + -0.4 = -0.533853913 Simplifying x + -0.4 = -0.533853913 Reorder the terms: -0.4 + x = -0.533853913 Solving -0.4 + x = -0.533853913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.533853913 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.533853913 + 0.4 x = -0.533853913 + 0.4 Combine like terms: -0.533853913 + 0.4 = -0.133853913 x = -0.133853913 Simplifying x = -0.133853913Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.933853913, -0.133853913}
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