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Simplifying 10x2 + -42x + 9 = 0 Reorder the terms: 9 + -42x + 10x2 = 0 Solving 9 + -42x + 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 + -4.2x + x2 = 0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + -4.2x + -0.9 + x2 = 0 + -0.9 Reorder the terms: 0.9 + -0.9 + -4.2x + x2 = 0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + -4.2x + x2 = 0 + -0.9 -4.2x + x2 = 0 + -0.9 Combine like terms: 0 + -0.9 = -0.9 -4.2x + x2 = -0.9 The x term is -4.2x. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2x + 4.41 + x2 = -0.9 + 4.41 Reorder the terms: 4.41 + -4.2x + x2 = -0.9 + 4.41 Combine like terms: -0.9 + 4.41 = 3.51 4.41 + -4.2x + x2 = 3.51 Factor a perfect square on the left side: (x + -2.1)(x + -2.1) = 3.51 Calculate the square root of the right side: 1.8734994 Break this problem into two subproblems by setting (x + -2.1) equal to 1.8734994 and -1.8734994.Subproblem 1
x + -2.1 = 1.8734994 Simplifying x + -2.1 = 1.8734994 Reorder the terms: -2.1 + x = 1.8734994 Solving -2.1 + x = 1.8734994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = 1.8734994 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = 1.8734994 + 2.1 x = 1.8734994 + 2.1 Combine like terms: 1.8734994 + 2.1 = 3.9734994 x = 3.9734994 Simplifying x = 3.9734994Subproblem 2
x + -2.1 = -1.8734994 Simplifying x + -2.1 = -1.8734994 Reorder the terms: -2.1 + x = -1.8734994 Solving -2.1 + x = -1.8734994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = -1.8734994 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = -1.8734994 + 2.1 x = -1.8734994 + 2.1 Combine like terms: -1.8734994 + 2.1 = 0.2265006 x = 0.2265006 Simplifying x = 0.2265006Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9734994, 0.2265006}
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