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Simplifying 10(x + -1) * 2x + 10x = 5 Reorder the terms: 10(-1 + x) * 2x + 10x = 5 Reorder the terms for easier multiplication: 10 * 2x(-1 + x) + 10x = 5 Multiply 10 * 2 20x(-1 + x) + 10x = 5 (-1 * 20x + x * 20x) + 10x = 5 (-20x + 20x2) + 10x = 5 Reorder the terms: -20x + 10x + 20x2 = 5 Combine like terms: -20x + 10x = -10x -10x + 20x2 = 5 Solving -10x + 20x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -10x + 20x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -10x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + -2x + 4x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -2x + 4x2)' equal to zero and attempt to solve: Simplifying -1 + -2x + 4x2 = 0 Solving -1 + -2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.5x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.5x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.5x + x2 = 0 + 0.25 -0.5x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.5x + x2 = 0.25 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 = 0.25 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.25 + 0.0625 Combine like terms: 0.25 + 0.0625 = 0.3125 0.0625 + -0.5x + x2 = 0.3125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (x + -0.25) equal to 0.559016994 and -0.559016994.Subproblem 1
x + -0.25 = 0.559016994 Simplifying x + -0.25 = 0.559016994 Reorder the terms: -0.25 + x = 0.559016994 Solving -0.25 + x = 0.559016994 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 = 0.559016994 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.559016994 + 0.25 x = 0.559016994 + 0.25 Combine like terms: 0.559016994 + 0.25 = 0.809016994 x = 0.809016994 Simplifying x = 0.809016994Subproblem 2
x + -0.25 = -0.559016994 Simplifying x + -0.25 = -0.559016994 Reorder the terms: -0.25 + x = -0.559016994 Solving -0.25 + x = -0.559016994 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 = -0.559016994 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.559016994 + 0.25 x = -0.559016994 + 0.25 Combine like terms: -0.559016994 + 0.25 = -0.309016994 x = -0.309016994 Simplifying x = -0.309016994Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.809016994, -0.309016994}Solution
x = {0.809016994, -0.309016994}
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