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Simplifying (2x + -8)(4x + -7) = x Reorder the terms: (-8 + 2x)(4x + -7) = x Reorder the terms: (-8 + 2x)(-7 + 4x) = x Multiply (-8 + 2x) * (-7 + 4x) (-8(-7 + 4x) + 2x * (-7 + 4x)) = x ((-7 * -8 + 4x * -8) + 2x * (-7 + 4x)) = x ((56 + -32x) + 2x * (-7 + 4x)) = x (56 + -32x + (-7 * 2x + 4x * 2x)) = x (56 + -32x + (-14x + 8x2)) = x Combine like terms: -32x + -14x = -46x (56 + -46x + 8x2) = x Solving 56 + -46x + 8x2 = x Solving for variable 'x'. Reorder the terms: 56 + -46x + -1x + 8x2 = x + -1x Combine like terms: -46x + -1x = -47x 56 + -47x + 8x2 = x + -1x Combine like terms: x + -1x = 0 56 + -47x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 7 + -5.875x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -5.875x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -5.875x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5.875x + x2 = 0 + -7 -5.875x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -5.875x + x2 = -7 The x term is -5.875x. Take half its coefficient (-2.9375). Square it (8.62890625) and add it to both sides. Add '8.62890625' to each side of the equation. -5.875x + 8.62890625 + x2 = -7 + 8.62890625 Reorder the terms: 8.62890625 + -5.875x + x2 = -7 + 8.62890625 Combine like terms: -7 + 8.62890625 = 1.62890625 8.62890625 + -5.875x + x2 = 1.62890625 Factor a perfect square on the left side: (x + -2.9375)(x + -2.9375) = 1.62890625 Calculate the square root of the right side: 1.276286116 Break this problem into two subproblems by setting (x + -2.9375) equal to 1.276286116 and -1.276286116.Subproblem 1
x + -2.9375 = 1.276286116 Simplifying x + -2.9375 = 1.276286116 Reorder the terms: -2.9375 + x = 1.276286116 Solving -2.9375 + x = 1.276286116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9375' to each side of the equation. -2.9375 + 2.9375 + x = 1.276286116 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + x = 1.276286116 + 2.9375 x = 1.276286116 + 2.9375 Combine like terms: 1.276286116 + 2.9375 = 4.213786116 x = 4.213786116 Simplifying x = 4.213786116Subproblem 2
x + -2.9375 = -1.276286116 Simplifying x + -2.9375 = -1.276286116 Reorder the terms: -2.9375 + x = -1.276286116 Solving -2.9375 + x = -1.276286116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9375' to each side of the equation. -2.9375 + 2.9375 + x = -1.276286116 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + x = -1.276286116 + 2.9375 x = -1.276286116 + 2.9375 Combine like terms: -1.276286116 + 2.9375 = 1.661213884 x = 1.661213884 Simplifying x = 1.661213884Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.213786116, 1.661213884}
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