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Simplifying 0 = -20x2 + 5x + 10 Reorder the terms: 0 = 10 + 5x + -20x2 Solving 0 = 10 + 5x + -20x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -5x + 20x2 = 10 + 5x + -20x2 + -10 + -5x + 20x2 Reorder the terms: -10 + -5x + 20x2 = 10 + -10 + 5x + -5x + -20x2 + 20x2 Combine like terms: 10 + -10 = 0 -10 + -5x + 20x2 = 0 + 5x + -5x + -20x2 + 20x2 -10 + -5x + 20x2 = 5x + -5x + -20x2 + 20x2 Combine like terms: 5x + -5x = 0 -10 + -5x + 20x2 = 0 + -20x2 + 20x2 -10 + -5x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 -10 + -5x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + -1x + 4x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1x + 4x2)' equal to zero and attempt to solve: Simplifying -2 + -1x + 4x2 = 0 Solving -2 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.25x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.25x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.25x + x2 = 0 + 0.5 -0.25x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.25x + x2 = 0.5 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.5 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.5 + 0.015625 Combine like terms: 0.5 + 0.015625 = 0.515625 0.015625 + -0.25x + x2 = 0.515625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (x + -0.125) equal to 0.718070331 and -0.718070331.Subproblem 1
x + -0.125 = 0.718070331 Simplifying x + -0.125 = 0.718070331 Reorder the terms: -0.125 + x = 0.718070331 Solving -0.125 + x = 0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.718070331 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.718070331 + 0.125 x = 0.718070331 + 0.125 Combine like terms: 0.718070331 + 0.125 = 0.843070331 x = 0.843070331 Simplifying x = 0.843070331Subproblem 2
x + -0.125 = -0.718070331 Simplifying x + -0.125 = -0.718070331 Reorder the terms: -0.125 + x = -0.718070331 Solving -0.125 + x = -0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.718070331 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.718070331 + 0.125 x = -0.718070331 + 0.125 Combine like terms: -0.718070331 + 0.125 = -0.593070331 x = -0.593070331 Simplifying x = -0.593070331Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.843070331, -0.593070331}Solution
x = {0.843070331, -0.593070331}
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