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Simplifying -8x(x + 2) + 4x + 6 = 6x + 7 Reorder the terms: -8x(2 + x) + 4x + 6 = 6x + 7 (2 * -8x + x * -8x) + 4x + 6 = 6x + 7 (-16x + -8x2) + 4x + 6 = 6x + 7 Reorder the terms: 6 + -16x + 4x + -8x2 = 6x + 7 Combine like terms: -16x + 4x = -12x 6 + -12x + -8x2 = 6x + 7 Reorder the terms: 6 + -12x + -8x2 = 7 + 6x Solving 6 + -12x + -8x2 = 7 + 6x Solving for variable 'x'. Reorder the terms: 6 + -7 + -12x + -6x + -8x2 = 7 + 6x + -7 + -6x Combine like terms: 6 + -7 = -1 -1 + -12x + -6x + -8x2 = 7 + 6x + -7 + -6x Combine like terms: -12x + -6x = -18x -1 + -18x + -8x2 = 7 + 6x + -7 + -6x Reorder the terms: -1 + -18x + -8x2 = 7 + -7 + 6x + -6x Combine like terms: 7 + -7 = 0 -1 + -18x + -8x2 = 0 + 6x + -6x -1 + -18x + -8x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -1 + -18x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 18x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 18x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + 18x + 8x2 = 0 Solving 1 + 18x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + 2.25x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 2.25x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 2.25x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 2.25x + x2 = 0 + -0.125 2.25x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 2.25x + x2 = -0.125 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = -0.125 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = -0.125 + 1.265625 Combine like terms: -0.125 + 1.265625 = 1.140625 1.265625 + 2.25x + x2 = 1.140625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + 1.125) equal to 1.068000468 and -1.068000468.Subproblem 1
x + 1.125 = 1.068000468 Simplifying x + 1.125 = 1.068000468 Reorder the terms: 1.125 + x = 1.068000468 Solving 1.125 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 1.068000468 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.068000468 + -1.125 x = 1.068000468 + -1.125 Combine like terms: 1.068000468 + -1.125 = -0.056999532 x = -0.056999532 Simplifying x = -0.056999532Subproblem 2
x + 1.125 = -1.068000468 Simplifying x + 1.125 = -1.068000468 Reorder the terms: 1.125 + x = -1.068000468 Solving 1.125 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -1.068000468 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.068000468 + -1.125 x = -1.068000468 + -1.125 Combine like terms: -1.068000468 + -1.125 = -2.193000468 x = -2.193000468 Simplifying x = -2.193000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.056999532, -2.193000468}Solution
x = {-0.056999532, -2.193000468}
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