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Simplifying 10x3 + -5x = 8x + -10x2 Reorder the terms: -5x + 10x3 = 8x + -10x2 Solving -5x + 10x3 = 8x + -10x2 Solving for variable 'x'. Reorder the terms: -5x + -8x + 10x2 + 10x3 = 8x + -10x2 + -8x + 10x2 Combine like terms: -5x + -8x = -13x -13x + 10x2 + 10x3 = 8x + -10x2 + -8x + 10x2 Reorder the terms: -13x + 10x2 + 10x3 = 8x + -8x + -10x2 + 10x2 Combine like terms: 8x + -8x = 0 -13x + 10x2 + 10x3 = 0 + -10x2 + 10x2 -13x + 10x2 + 10x3 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 -13x + 10x2 + 10x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-13 + 10x + 10x2) = 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 '(-13 + 10x + 10x2)' equal to zero and attempt to solve: Simplifying -13 + 10x + 10x2 = 0 Solving -13 + 10x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.3 + x + x2 = 0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + x + 1.3 + x2 = 0 + 1.3 Reorder the terms: -1.3 + 1.3 + x + x2 = 0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x + x2 = 0 + 1.3 x + x2 = 0 + 1.3 Combine like terms: 0 + 1.3 = 1.3 x + x2 = 1.3 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. + 0.25 + x2 = 1.3 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.3 + 0.25 Combine like terms: 1.3 + 0.25 = 1.55 1.25 + x2 = 1.55 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.55 Calculate the square root of the right side: 1.24498996 Break this problem into two subproblems by setting (x + 0.5) equal to 1.24498996 and -1.24498996.Subproblem 1
x + 0.5 = 1.24498996 Simplifying x + 0.5 = 1.24498996 Reorder the terms: 0.5 + x = 1.24498996 Solving 0.5 + x = 1.24498996 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 = 1.24498996 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.24498996 + -0.5 x = 1.24498996 + -0.5 Combine like terms: 1.24498996 + -0.5 = 0.74498996 x = 0.74498996 Simplifying x = 0.74498996Subproblem 2
x + 0.5 = -1.24498996 Simplifying x + 0.5 = -1.24498996 Reorder the terms: 0.5 + x = -1.24498996 Solving 0.5 + x = -1.24498996 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 = -1.24498996 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.24498996 + -0.5 x = -1.24498996 + -0.5 Combine like terms: -1.24498996 + -0.5 = -1.74498996 x = -1.74498996 Simplifying x = -1.74498996Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.74498996, -1.74498996}Solution
x = {0, 0.74498996, -1.74498996}
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