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Simplifying 2x(10x2 + 7x + -2) = 0 Reorder the terms: 2x(-2 + 7x + 10x2) = 0 (-2 * 2x + 7x * 2x + 10x2 * 2x) = 0 (-4x + 14x2 + 20x3) = 0 Solving -4x + 14x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-2 + 7x + 10x2) = 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 '(-2 + 7x + 10x2)' equal to zero and attempt to solve: Simplifying -2 + 7x + 10x2 = 0 Solving -2 + 7x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + 0.7x + x2 = 0.0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.7x + 0.2 + x2 = 0.0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.7x + x2 = 0.0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.7x + x2 = 0.0 + 0.2 0.7x + x2 = 0.0 + 0.2 Combine like terms: 0.0 + 0.2 = 0.2 0.7x + x2 = 0.2 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = 0.2 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 0.2 + 0.1225 Combine like terms: 0.2 + 0.1225 = 0.3225 0.1225 + 0.7x + x2 = 0.3225 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 0.3225 Calculate the square root of the right side: 0.567890835 Break this problem into two subproblems by setting (x + 0.35) equal to 0.567890835 and -0.567890835.Subproblem 1
x + 0.35 = 0.567890835 Simplifying x + 0.35 = 0.567890835 Reorder the terms: 0.35 + x = 0.567890835 Solving 0.35 + x = 0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 0.567890835 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.567890835 + -0.35 x = 0.567890835 + -0.35 Combine like terms: 0.567890835 + -0.35 = 0.217890835 x = 0.217890835 Simplifying x = 0.217890835Subproblem 2
x + 0.35 = -0.567890835 Simplifying x + 0.35 = -0.567890835 Reorder the terms: 0.35 + x = -0.567890835 Solving 0.35 + x = -0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -0.567890835 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.567890835 + -0.35 x = -0.567890835 + -0.35 Combine like terms: -0.567890835 + -0.35 = -0.917890835 x = -0.917890835 Simplifying x = -0.917890835Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.217890835, -0.917890835}Solution
x = {0, 0.217890835, -0.917890835}
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