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Simplifying 10x2 + -20x + 9 = 0 Reorder the terms: 9 + -20x + 10x2 = 0 Solving 9 + -20x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.9 + -2x + x2 = 0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + -2x + -0.9 + x2 = 0 + -0.9 Reorder the terms: 0.9 + -0.9 + -2x + x2 = 0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + -2x + x2 = 0 + -0.9 -2x + x2 = 0 + -0.9 Combine like terms: 0 + -0.9 = -0.9 -2x + x2 = -0.9 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.9 + 1 Reorder the terms: 1 + -2x + x2 = -0.9 + 1 Combine like terms: -0.9 + 1 = 0.1 1 + -2x + x2 = 0.1 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.1 Calculate the square root of the right side: 0.316227766 Break this problem into two subproblems by setting (x + -1) equal to 0.316227766 and -0.316227766.Subproblem 1
x + -1 = 0.316227766 Simplifying x + -1 = 0.316227766 Reorder the terms: -1 + x = 0.316227766 Solving -1 + x = 0.316227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.316227766 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.316227766 + 1 x = 0.316227766 + 1 Combine like terms: 0.316227766 + 1 = 1.316227766 x = 1.316227766 Simplifying x = 1.316227766Subproblem 2
x + -1 = -0.316227766 Simplifying x + -1 = -0.316227766 Reorder the terms: -1 + x = -0.316227766 Solving -1 + x = -0.316227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.316227766 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.316227766 + 1 x = -0.316227766 + 1 Combine like terms: -0.316227766 + 1 = 0.683772234 x = 0.683772234 Simplifying x = 0.683772234Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.316227766, 0.683772234}
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