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Simplifying (4x3 + -3x2 + 5x) + (6x3 + 5x2 + -10x) = 0 Reorder the terms: (5x + -3x2 + 4x3) + (6x3 + 5x2 + -10x) = 0 Remove parenthesis around (5x + -3x2 + 4x3) 5x + -3x2 + 4x3 + (6x3 + 5x2 + -10x) = 0 Reorder the terms: 5x + -3x2 + 4x3 + (-10x + 5x2 + 6x3) = 0 Remove parenthesis around (-10x + 5x2 + 6x3) 5x + -3x2 + 4x3 + -10x + 5x2 + 6x3 = 0 Reorder the terms: 5x + -10x + -3x2 + 5x2 + 4x3 + 6x3 = 0 Combine like terms: 5x + -10x = -5x -5x + -3x2 + 5x2 + 4x3 + 6x3 = 0 Combine like terms: -3x2 + 5x2 = 2x2 -5x + 2x2 + 4x3 + 6x3 = 0 Combine like terms: 4x3 + 6x3 = 10x3 -5x + 2x2 + 10x3 = 0 Solving -5x + 2x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 2x + 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 '(-5 + 2x + 10x2)' equal to zero and attempt to solve: Simplifying -5 + 2x + 10x2 = 0 Solving -5 + 2x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.2x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.2x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.2x + x2 = 0.0 + 0.5 0.2x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 0.2x + x2 = 0.5 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.5 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.5 + 0.01 Combine like terms: 0.5 + 0.01 = 0.51 0.01 + 0.2x + x2 = 0.51 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.51 Calculate the square root of the right side: 0.714142843 Break this problem into two subproblems by setting (x + 0.1) equal to 0.714142843 and -0.714142843.Subproblem 1
x + 0.1 = 0.714142843 Simplifying x + 0.1 = 0.714142843 Reorder the terms: 0.1 + x = 0.714142843 Solving 0.1 + x = 0.714142843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.714142843 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.714142843 + -0.1 x = 0.714142843 + -0.1 Combine like terms: 0.714142843 + -0.1 = 0.614142843 x = 0.614142843 Simplifying x = 0.614142843Subproblem 2
x + 0.1 = -0.714142843 Simplifying x + 0.1 = -0.714142843 Reorder the terms: 0.1 + x = -0.714142843 Solving 0.1 + x = -0.714142843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.714142843 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.714142843 + -0.1 x = -0.714142843 + -0.1 Combine like terms: -0.714142843 + -0.1 = -0.814142843 x = -0.814142843 Simplifying x = -0.814142843Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.614142843, -0.814142843}Solution
x = {0, 0.614142843, -0.814142843}
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