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Simplifying 8x3 + 2x2 + -30x = 0 Reorder the terms: -30x + 2x2 + 8x3 = 0 Solving -30x + 2x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-15 + x + 4x2) = 0 Ignore the factor 2.Subproblem 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 '(-15 + x + 4x2)' equal to zero and attempt to solve: Simplifying -15 + x + 4x2 = 0 Solving -15 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 0.25x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 0.25x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 0.25x + x2 = 0 + 3.75 0.25x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 0.25x + x2 = 3.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25x + 0.25 + x2 = 3.75 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 3.75 + 0.25 Combine like terms: 3.75 + 0.25 = 4 0.25 + 0.25x + x2 = 4 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + 0.5) equal to 2 and -2.Subproblem 1
x + 0.5 = 2 Simplifying x + 0.5 = 2 Reorder the terms: 0.5 + x = 2 Solving 0.5 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2 + -0.5 x = 2 + -0.5 Combine like terms: 2 + -0.5 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + 0.5 = -2 Simplifying x + 0.5 = -2 Reorder the terms: 0.5 + x = -2 Solving 0.5 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2 + -0.5 x = -2 + -0.5 Combine like terms: -2 + -0.5 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, -2.5}Solution
x = {0, 1.5, -2.5}
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