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Simplifying 8x4 + 9x3 + -6x2 = 0 Reorder the terms: -6x2 + 9x3 + 8x4 = 0 Solving -6x2 + 9x3 + 8x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-6 + 9x + 8x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-6 + 9x + 8x2)' equal to zero and attempt to solve: Simplifying -6 + 9x + 8x2 = 0 Solving -6 + 9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + 1.125x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.125x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.125x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.125x + x2 = 0 + 0.75 1.125x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.125x + x2 = 0.75 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 = 0.75 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 0.75 + 0.31640625 Combine like terms: 0.75 + 0.31640625 = 1.06640625 0.31640625 + 1.125x + x2 = 1.06640625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 1.06640625 Calculate the square root of the right side: 1.032669478 Break this problem into two subproblems by setting (x + 0.5625) equal to 1.032669478 and -1.032669478.Subproblem 1
x + 0.5625 = 1.032669478 Simplifying x + 0.5625 = 1.032669478 Reorder the terms: 0.5625 + x = 1.032669478 Solving 0.5625 + x = 1.032669478 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 = 1.032669478 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 1.032669478 + -0.5625 x = 1.032669478 + -0.5625 Combine like terms: 1.032669478 + -0.5625 = 0.470169478 x = 0.470169478 Simplifying x = 0.470169478Subproblem 2
x + 0.5625 = -1.032669478 Simplifying x + 0.5625 = -1.032669478 Reorder the terms: 0.5625 + x = -1.032669478 Solving 0.5625 + x = -1.032669478 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 = -1.032669478 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -1.032669478 + -0.5625 x = -1.032669478 + -0.5625 Combine like terms: -1.032669478 + -0.5625 = -1.595169478 x = -1.595169478 Simplifying x = -1.595169478Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.470169478, -1.595169478}Solution
x = {0, 0.470169478, -1.595169478}
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