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Simplifying 8x(x + -8) = 2x + 8 Reorder the terms: 8x(-8 + x) = 2x + 8 (-8 * 8x + x * 8x) = 2x + 8 (-64x + 8x2) = 2x + 8 Reorder the terms: -64x + 8x2 = 8 + 2x Solving -64x + 8x2 = 8 + 2x Solving for variable 'x'. Reorder the terms: -8 + -64x + -2x + 8x2 = 8 + 2x + -8 + -2x Combine like terms: -64x + -2x = -66x -8 + -66x + 8x2 = 8 + 2x + -8 + -2x Reorder the terms: -8 + -66x + 8x2 = 8 + -8 + 2x + -2x Combine like terms: 8 + -8 = 0 -8 + -66x + 8x2 = 0 + 2x + -2x -8 + -66x + 8x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -8 + -66x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -33x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -33x + 4x2)' equal to zero and attempt to solve: Simplifying -4 + -33x + 4x2 = 0 Solving -4 + -33x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -8.25x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -8.25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -8.25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8.25x + x2 = 0 + 1 -8.25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -8.25x + x2 = 1 The x term is -8.25x. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25x + 17.015625 + x2 = 1 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = 1 + 17.015625 Combine like terms: 1 + 17.015625 = 18.015625 17.015625 + -8.25x + x2 = 18.015625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 18.015625 Calculate the square root of the right side: 4.244481712 Break this problem into two subproblems by setting (x + -4.125) equal to 4.244481712 and -4.244481712.Subproblem 1
x + -4.125 = 4.244481712 Simplifying x + -4.125 = 4.244481712 Reorder the terms: -4.125 + x = 4.244481712 Solving -4.125 + x = 4.244481712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = 4.244481712 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 4.244481712 + 4.125 x = 4.244481712 + 4.125 Combine like terms: 4.244481712 + 4.125 = 8.369481712 x = 8.369481712 Simplifying x = 8.369481712Subproblem 2
x + -4.125 = -4.244481712 Simplifying x + -4.125 = -4.244481712 Reorder the terms: -4.125 + x = -4.244481712 Solving -4.125 + x = -4.244481712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = -4.244481712 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -4.244481712 + 4.125 x = -4.244481712 + 4.125 Combine like terms: -4.244481712 + 4.125 = -0.119481712 x = -0.119481712 Simplifying x = -0.119481712Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.369481712, -0.119481712}Solution
x = {8.369481712, -0.119481712}
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