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Simplifying -8x(x + 4) + 4x + 7 = 7x + 10 Reorder the terms: -8x(4 + x) + 4x + 7 = 7x + 10 (4 * -8x + x * -8x) + 4x + 7 = 7x + 10 (-32x + -8x2) + 4x + 7 = 7x + 10 Reorder the terms: 7 + -32x + 4x + -8x2 = 7x + 10 Combine like terms: -32x + 4x = -28x 7 + -28x + -8x2 = 7x + 10 Reorder the terms: 7 + -28x + -8x2 = 10 + 7x Solving 7 + -28x + -8x2 = 10 + 7x Solving for variable 'x'. Reorder the terms: 7 + -10 + -28x + -7x + -8x2 = 10 + 7x + -10 + -7x Combine like terms: 7 + -10 = -3 -3 + -28x + -7x + -8x2 = 10 + 7x + -10 + -7x Combine like terms: -28x + -7x = -35x -3 + -35x + -8x2 = 10 + 7x + -10 + -7x Reorder the terms: -3 + -35x + -8x2 = 10 + -10 + 7x + -7x Combine like terms: 10 + -10 = 0 -3 + -35x + -8x2 = 0 + 7x + -7x -3 + -35x + -8x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -3 + -35x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 35x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 35x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 35x + 8x2 = 0 Solving 3 + 35x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 4.375x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 4.375x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 4.375x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 4.375x + x2 = 0 + -0.375 4.375x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 4.375x + x2 = -0.375 The x term is 4.375x. Take half its coefficient (2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. 4.375x + 4.78515625 + x2 = -0.375 + 4.78515625 Reorder the terms: 4.78515625 + 4.375x + x2 = -0.375 + 4.78515625 Combine like terms: -0.375 + 4.78515625 = 4.41015625 4.78515625 + 4.375x + x2 = 4.41015625 Factor a perfect square on the left side: (x + 2.1875)(x + 2.1875) = 4.41015625 Calculate the square root of the right side: 2.100037202 Break this problem into two subproblems by setting (x + 2.1875) equal to 2.100037202 and -2.100037202.Subproblem 1
x + 2.1875 = 2.100037202 Simplifying x + 2.1875 = 2.100037202 Reorder the terms: 2.1875 + x = 2.100037202 Solving 2.1875 + x = 2.100037202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + x = 2.100037202 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + x = 2.100037202 + -2.1875 x = 2.100037202 + -2.1875 Combine like terms: 2.100037202 + -2.1875 = -0.087462798 x = -0.087462798 Simplifying x = -0.087462798Subproblem 2
x + 2.1875 = -2.100037202 Simplifying x + 2.1875 = -2.100037202 Reorder the terms: 2.1875 + x = -2.100037202 Solving 2.1875 + x = -2.100037202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + x = -2.100037202 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + x = -2.100037202 + -2.1875 x = -2.100037202 + -2.1875 Combine like terms: -2.100037202 + -2.1875 = -4.287537202 x = -4.287537202 Simplifying x = -4.287537202Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.087462798, -4.287537202}Solution
x = {-0.087462798, -4.287537202}
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