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Simplifying 23.8x2 + 7x + -1 = 0 Reorder the terms: -1 + 7x + 23.8x2 = 0 Solving -1 + 7x + 23.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23.8 the coefficient of the squared term: Divide each side by '23.8'. -0.04201680672 + 0.2941176471x + x2 = 0 Move the constant term to the right: Add '0.04201680672' to each side of the equation. -0.04201680672 + 0.2941176471x + 0.04201680672 + x2 = 0 + 0.04201680672 Reorder the terms: -0.04201680672 + 0.04201680672 + 0.2941176471x + x2 = 0 + 0.04201680672 Combine like terms: -0.04201680672 + 0.04201680672 = 0.00000000000 0.00000000000 + 0.2941176471x + x2 = 0 + 0.04201680672 0.2941176471x + x2 = 0 + 0.04201680672 Combine like terms: 0 + 0.04201680672 = 0.04201680672 0.2941176471x + x2 = 0.04201680672 The x term is 0.2941176471x. Take half its coefficient (0.1470588236). Square it (0.02162629760) and add it to both sides. Add '0.02162629760' to each side of the equation. 0.2941176471x + 0.02162629760 + x2 = 0.04201680672 + 0.02162629760 Reorder the terms: 0.02162629760 + 0.2941176471x + x2 = 0.04201680672 + 0.02162629760 Combine like terms: 0.04201680672 + 0.02162629760 = 0.06364310432 0.02162629760 + 0.2941176471x + x2 = 0.06364310432 Factor a perfect square on the left side: (x + 0.1470588236)(x + 0.1470588236) = 0.06364310432 Calculate the square root of the right side: 0.25227585 Break this problem into two subproblems by setting (x + 0.1470588236) equal to 0.25227585 and -0.25227585.Subproblem 1
x + 0.1470588236 = 0.25227585 Simplifying x + 0.1470588236 = 0.25227585 Reorder the terms: 0.1470588236 + x = 0.25227585 Solving 0.1470588236 + x = 0.25227585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1470588236' to each side of the equation. 0.1470588236 + -0.1470588236 + x = 0.25227585 + -0.1470588236 Combine like terms: 0.1470588236 + -0.1470588236 = 0.0000000000 0.0000000000 + x = 0.25227585 + -0.1470588236 x = 0.25227585 + -0.1470588236 Combine like terms: 0.25227585 + -0.1470588236 = 0.1052170264 x = 0.1052170264 Simplifying x = 0.1052170264Subproblem 2
x + 0.1470588236 = -0.25227585 Simplifying x + 0.1470588236 = -0.25227585 Reorder the terms: 0.1470588236 + x = -0.25227585 Solving 0.1470588236 + x = -0.25227585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1470588236' to each side of the equation. 0.1470588236 + -0.1470588236 + x = -0.25227585 + -0.1470588236 Combine like terms: 0.1470588236 + -0.1470588236 = 0.0000000000 0.0000000000 + x = -0.25227585 + -0.1470588236 x = -0.25227585 + -0.1470588236 Combine like terms: -0.25227585 + -0.1470588236 = -0.3993346736 x = -0.3993346736 Simplifying x = -0.3993346736Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1052170264, -0.3993346736}
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