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Simplifying x = (x + 8)(2x + -8) Reorder the terms: x = (8 + x)(2x + -8) Reorder the terms: x = (8 + x)(-8 + 2x) Multiply (8 + x) * (-8 + 2x) x = (8(-8 + 2x) + x(-8 + 2x)) x = ((-8 * 8 + 2x * 8) + x(-8 + 2x)) x = ((-64 + 16x) + x(-8 + 2x)) x = (-64 + 16x + (-8 * x + 2x * x)) x = (-64 + 16x + (-8x + 2x2)) Combine like terms: 16x + -8x = 8x x = (-64 + 8x + 2x2) Solving x = -64 + 8x + 2x2 Solving for variable 'x'. Reorder the terms: 64 + x + -8x + -2x2 = -64 + 8x + 2x2 + 64 + -8x + -2x2 Combine like terms: x + -8x = -7x 64 + -7x + -2x2 = -64 + 8x + 2x2 + 64 + -8x + -2x2 Reorder the terms: 64 + -7x + -2x2 = -64 + 64 + 8x + -8x + 2x2 + -2x2 Combine like terms: -64 + 64 = 0 64 + -7x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2 64 + -7x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 64 + -7x + -2x2 = 0 + 2x2 + -2x2 64 + -7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 64 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -32 + 3.5x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 3.5x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 3.5x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 3.5x + x2 = 0 + 32 3.5x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 3.5x + x2 = 32 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 32 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 32 + 3.0625 Combine like terms: 32 + 3.0625 = 35.0625 3.0625 + 3.5x + x2 = 35.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 35.0625 Calculate the square root of the right side: 5.921359641 Break this problem into two subproblems by setting (x + 1.75) equal to 5.921359641 and -5.921359641.Subproblem 1
x + 1.75 = 5.921359641 Simplifying x + 1.75 = 5.921359641 Reorder the terms: 1.75 + x = 5.921359641 Solving 1.75 + x = 5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 5.921359641 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 5.921359641 + -1.75 x = 5.921359641 + -1.75 Combine like terms: 5.921359641 + -1.75 = 4.171359641 x = 4.171359641 Simplifying x = 4.171359641Subproblem 2
x + 1.75 = -5.921359641 Simplifying x + 1.75 = -5.921359641 Reorder the terms: 1.75 + x = -5.921359641 Solving 1.75 + x = -5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -5.921359641 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -5.921359641 + -1.75 x = -5.921359641 + -1.75 Combine like terms: -5.921359641 + -1.75 = -7.671359641 x = -7.671359641 Simplifying x = -7.671359641Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.171359641, -7.671359641}
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