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Simplifying 20x2 + -10x + -9 = 0 Reorder the terms: -9 + -10x + 20x2 = 0 Solving -9 + -10x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.45 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + -0.5x + 0.45 + x2 = 0 + 0.45 Reorder the terms: -0.45 + 0.45 + -0.5x + x2 = 0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + -0.5x + x2 = 0 + 0.45 -0.5x + x2 = 0 + 0.45 Combine like terms: 0 + 0.45 = 0.45 -0.5x + x2 = 0.45 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 = 0.45 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.45 + 0.0625 Combine like terms: 0.45 + 0.0625 = 0.5125 0.0625 + -0.5x + x2 = 0.5125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.5125 Calculate the square root of the right side: 0.715891053 Break this problem into two subproblems by setting (x + -0.25) equal to 0.715891053 and -0.715891053.Subproblem 1
x + -0.25 = 0.715891053 Simplifying x + -0.25 = 0.715891053 Reorder the terms: -0.25 + x = 0.715891053 Solving -0.25 + x = 0.715891053 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 = 0.715891053 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.715891053 + 0.25 x = 0.715891053 + 0.25 Combine like terms: 0.715891053 + 0.25 = 0.965891053 x = 0.965891053 Simplifying x = 0.965891053Subproblem 2
x + -0.25 = -0.715891053 Simplifying x + -0.25 = -0.715891053 Reorder the terms: -0.25 + x = -0.715891053 Solving -0.25 + x = -0.715891053 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 = -0.715891053 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.715891053 + 0.25 x = -0.715891053 + 0.25 Combine like terms: -0.715891053 + 0.25 = -0.465891053 x = -0.465891053 Simplifying x = -0.465891053Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.965891053, -0.465891053}
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