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Simplifying (8x3 + 6x + -4) + (9x2 + -7x + 4) = 0 Reorder the terms: (-4 + 6x + 8x3) + (9x2 + -7x + 4) = 0 Remove parenthesis around (-4 + 6x + 8x3) -4 + 6x + 8x3 + (9x2 + -7x + 4) = 0 Reorder the terms: -4 + 6x + 8x3 + (4 + -7x + 9x2) = 0 Remove parenthesis around (4 + -7x + 9x2) -4 + 6x + 8x3 + 4 + -7x + 9x2 = 0 Reorder the terms: -4 + 4 + 6x + -7x + 9x2 + 8x3 = 0 Combine like terms: -4 + 4 = 0 0 + 6x + -7x + 9x2 + 8x3 = 0 6x + -7x + 9x2 + 8x3 = 0 Combine like terms: 6x + -7x = -1x -1x + 9x2 + 8x3 = 0 Solving -1x + 9x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 9x + 8x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1 + 9x + 8x2)' equal to zero and attempt to solve: Simplifying -1 + 9x + 8x2 = 0 Solving -1 + 9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + 1.125x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 1.125x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 1.125x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 1.125x + x2 = 0 + 0.125 1.125x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 1.125x + x2 = 0.125 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = 0.125 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 0.125 + 0.31640625 Combine like terms: 0.125 + 0.31640625 = 0.44140625 0.31640625 + 1.125x + x2 = 0.44140625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 0.44140625 Calculate the square root of the right side: 0.664384113 Break this problem into two subproblems by setting (x + 0.5625) equal to 0.664384113 and -0.664384113.Subproblem 1
x + 0.5625 = 0.664384113 Simplifying x + 0.5625 = 0.664384113 Reorder the terms: 0.5625 + x = 0.664384113 Solving 0.5625 + x = 0.664384113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 0.664384113 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 0.664384113 + -0.5625 x = 0.664384113 + -0.5625 Combine like terms: 0.664384113 + -0.5625 = 0.101884113 x = 0.101884113 Simplifying x = 0.101884113Subproblem 2
x + 0.5625 = -0.664384113 Simplifying x + 0.5625 = -0.664384113 Reorder the terms: 0.5625 + x = -0.664384113 Solving 0.5625 + x = -0.664384113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -0.664384113 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -0.664384113 + -0.5625 x = -0.664384113 + -0.5625 Combine like terms: -0.664384113 + -0.5625 = -1.226884113 x = -1.226884113 Simplifying x = -1.226884113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.101884113, -1.226884113}Solution
x = {0, 0.101884113, -1.226884113}
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