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Simplifying (2x + -1)(8x + -12) = 35 Reorder the terms: (-1 + 2x)(8x + -12) = 35 Reorder the terms: (-1 + 2x)(-12 + 8x) = 35 Multiply (-1 + 2x) * (-12 + 8x) (-1(-12 + 8x) + 2x * (-12 + 8x)) = 35 ((-12 * -1 + 8x * -1) + 2x * (-12 + 8x)) = 35 ((12 + -8x) + 2x * (-12 + 8x)) = 35 (12 + -8x + (-12 * 2x + 8x * 2x)) = 35 (12 + -8x + (-24x + 16x2)) = 35 Combine like terms: -8x + -24x = -32x (12 + -32x + 16x2) = 35 Solving 12 + -32x + 16x2 = 35 Solving for variable 'x'. Reorder the terms: 12 + -35 + -32x + 16x2 = 35 + -35 Combine like terms: 12 + -35 = -23 -23 + -32x + 16x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -23 + -32x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.4375 + -2x + x2 = 0 Move the constant term to the right: Add '1.4375' to each side of the equation. -1.4375 + -2x + 1.4375 + x2 = 0 + 1.4375 Reorder the terms: -1.4375 + 1.4375 + -2x + x2 = 0 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + -2x + x2 = 0 + 1.4375 -2x + x2 = 0 + 1.4375 Combine like terms: 0 + 1.4375 = 1.4375 -2x + x2 = 1.4375 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.4375 + 1 Reorder the terms: 1 + -2x + x2 = 1.4375 + 1 Combine like terms: 1.4375 + 1 = 2.4375 1 + -2x + x2 = 2.4375 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.4375 Calculate the square root of the right side: 1.5612495 Break this problem into two subproblems by setting (x + -1) equal to 1.5612495 and -1.5612495.Subproblem 1
x + -1 = 1.5612495 Simplifying x + -1 = 1.5612495 Reorder the terms: -1 + x = 1.5612495 Solving -1 + x = 1.5612495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.5612495 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.5612495 + 1 x = 1.5612495 + 1 Combine like terms: 1.5612495 + 1 = 2.5612495 x = 2.5612495 Simplifying x = 2.5612495Subproblem 2
x + -1 = -1.5612495 Simplifying x + -1 = -1.5612495 Reorder the terms: -1 + x = -1.5612495 Solving -1 + x = -1.5612495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.5612495 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.5612495 + 1 x = -1.5612495 + 1 Combine like terms: -1.5612495 + 1 = -0.5612495 x = -0.5612495 Simplifying x = -0.5612495Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5612495, -0.5612495}
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