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Simplifying 8x3 + 4x2 + -14x = 0 Reorder the terms: -14x + 4x2 + 8x3 = 0 Solving -14x + 4x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-7 + 2x + 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 '(-7 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying -7 + 2x + 4x2 = 0 Solving -7 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 0.5x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 0.5x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 0.5x + x2 = 0 + 1.75 0.5x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 0.5x + x2 = 1.75 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1.75 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.75 + 0.0625 Combine like terms: 1.75 + 0.0625 = 1.8125 0.0625 + 0.5x + x2 = 1.8125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (x + 0.25) equal to 1.346291202 and -1.346291202.Subproblem 1
x + 0.25 = 1.346291202 Simplifying x + 0.25 = 1.346291202 Reorder the terms: 0.25 + x = 1.346291202 Solving 0.25 + x = 1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.346291202 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.346291202 + -0.25 x = 1.346291202 + -0.25 Combine like terms: 1.346291202 + -0.25 = 1.096291202 x = 1.096291202 Simplifying x = 1.096291202Subproblem 2
x + 0.25 = -1.346291202 Simplifying x + 0.25 = -1.346291202 Reorder the terms: 0.25 + x = -1.346291202 Solving 0.25 + x = -1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.346291202 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.346291202 + -0.25 x = -1.346291202 + -0.25 Combine like terms: -1.346291202 + -0.25 = -1.596291202 x = -1.596291202 Simplifying x = -1.596291202Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.096291202, -1.596291202}Solution
x = {0, 1.096291202, -1.596291202}
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