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Simplifying 4.2[(8 + -1x)(4 + -1x)] = 0.25x Multiply (8 + -1x) * (4 + -1x) 4.2[(8(4 + -1x) + -1x * (4 + -1x))] = 0.25x 4.2[((4 * 8 + -1x * 8) + -1x * (4 + -1x))] = 0.25x 4.2[((32 + -8x) + -1x * (4 + -1x))] = 0.25x 4.2[(32 + -8x + (4 * -1x + -1x * -1x))] = 0.25x 4.2[(32 + -8x + (-4x + 1x2))] = 0.25x Combine like terms: -8x + -4x = -12x 4.2[(32 + -12x + 1x2)] = 0.25x [32 * 4.2 + -12x * 4.2 + 1x2 * 4.2] = 0.25x [134.4 + -50.4x + 4.2x2] = 0.25x Solving 134.4 + -50.4x + 4.2x2 = 0.25x Solving for variable 'x'. Reorder the terms: 134.4 + -50.4x + -0.25x + 4.2x2 = 0.25x + -0.25x Combine like terms: -50.4x + -0.25x = -50.65x 134.4 + -50.65x + 4.2x2 = 0.25x + -0.25x Combine like terms: 0.25x + -0.25x = 0.00 134.4 + -50.65x + 4.2x2 = 0.00 Begin completing the square. Divide all terms by 4.2 the coefficient of the squared term: Divide each side by '4.2'. 32 + -12.05952381x + x2 = 0.0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + -12.05952381x + -32 + x2 = 0.0 + -32 Reorder the terms: 32 + -32 + -12.05952381x + x2 = 0.0 + -32 Combine like terms: 32 + -32 = 0 0 + -12.05952381x + x2 = 0.0 + -32 -12.05952381x + x2 = 0.0 + -32 Combine like terms: 0.0 + -32 = -32 -12.05952381x + x2 = -32 The x term is -12.05952381x. Take half its coefficient (-6.029761905). Square it (36.35802863) and add it to both sides. Add '36.35802863' to each side of the equation. -12.05952381x + 36.35802863 + x2 = -32 + 36.35802863 Reorder the terms: 36.35802863 + -12.05952381x + x2 = -32 + 36.35802863 Combine like terms: -32 + 36.35802863 = 4.35802863 36.35802863 + -12.05952381x + x2 = 4.35802863 Factor a perfect square on the left side: (x + -6.029761905)(x + -6.029761905) = 4.35802863 Calculate the square root of the right side: 2.087589191 Break this problem into two subproblems by setting (x + -6.029761905) equal to 2.087589191 and -2.087589191.Subproblem 1
x + -6.029761905 = 2.087589191 Simplifying x + -6.029761905 = 2.087589191 Reorder the terms: -6.029761905 + x = 2.087589191 Solving -6.029761905 + x = 2.087589191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.029761905' to each side of the equation. -6.029761905 + 6.029761905 + x = 2.087589191 + 6.029761905 Combine like terms: -6.029761905 + 6.029761905 = 0.000000000 0.000000000 + x = 2.087589191 + 6.029761905 x = 2.087589191 + 6.029761905 Combine like terms: 2.087589191 + 6.029761905 = 8.117351096 x = 8.117351096 Simplifying x = 8.117351096Subproblem 2
x + -6.029761905 = -2.087589191 Simplifying x + -6.029761905 = -2.087589191 Reorder the terms: -6.029761905 + x = -2.087589191 Solving -6.029761905 + x = -2.087589191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.029761905' to each side of the equation. -6.029761905 + 6.029761905 + x = -2.087589191 + 6.029761905 Combine like terms: -6.029761905 + 6.029761905 = 0.000000000 0.000000000 + x = -2.087589191 + 6.029761905 x = -2.087589191 + 6.029761905 Combine like terms: -2.087589191 + 6.029761905 = 3.942172714 x = 3.942172714 Simplifying x = 3.942172714Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.117351096, 3.942172714}
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