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Simplifying 40x2 + 89x + 1 = 0 Reorder the terms: 1 + 89x + 40x2 = 0 Solving 1 + 89x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.025 + 2.225x + x2 = 0 Move the constant term to the right: Add '-0.025' to each side of the equation. 0.025 + 2.225x + -0.025 + x2 = 0 + -0.025 Reorder the terms: 0.025 + -0.025 + 2.225x + x2 = 0 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + 2.225x + x2 = 0 + -0.025 2.225x + x2 = 0 + -0.025 Combine like terms: 0 + -0.025 = -0.025 2.225x + x2 = -0.025 The x term is 2.225x. Take half its coefficient (1.1125). Square it (1.23765625) and add it to both sides. Add '1.23765625' to each side of the equation. 2.225x + 1.23765625 + x2 = -0.025 + 1.23765625 Reorder the terms: 1.23765625 + 2.225x + x2 = -0.025 + 1.23765625 Combine like terms: -0.025 + 1.23765625 = 1.21265625 1.23765625 + 2.225x + x2 = 1.21265625 Factor a perfect square on the left side: (x + 1.1125)(x + 1.1125) = 1.21265625 Calculate the square root of the right side: 1.101206724 Break this problem into two subproblems by setting (x + 1.1125) equal to 1.101206724 and -1.101206724.Subproblem 1
x + 1.1125 = 1.101206724 Simplifying x + 1.1125 = 1.101206724 Reorder the terms: 1.1125 + x = 1.101206724 Solving 1.1125 + x = 1.101206724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1125' to each side of the equation. 1.1125 + -1.1125 + x = 1.101206724 + -1.1125 Combine like terms: 1.1125 + -1.1125 = 0.0000 0.0000 + x = 1.101206724 + -1.1125 x = 1.101206724 + -1.1125 Combine like terms: 1.101206724 + -1.1125 = -0.011293276 x = -0.011293276 Simplifying x = -0.011293276Subproblem 2
x + 1.1125 = -1.101206724 Simplifying x + 1.1125 = -1.101206724 Reorder the terms: 1.1125 + x = -1.101206724 Solving 1.1125 + x = -1.101206724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1125' to each side of the equation. 1.1125 + -1.1125 + x = -1.101206724 + -1.1125 Combine like terms: 1.1125 + -1.1125 = 0.0000 0.0000 + x = -1.101206724 + -1.1125 x = -1.101206724 + -1.1125 Combine like terms: -1.101206724 + -1.1125 = -2.213706724 x = -2.213706724 Simplifying x = -2.213706724Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.011293276, -2.213706724}
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