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Simplifying (3x + 3.1)(3.1) * x = 7 Reorder the terms: (3.1 + 3x)(3.1) * x = 7 Reorder the terms for easier multiplication: 3.1x(3.1 + 3x) = 7 (3.1 * 3.1x + 3x * 3.1x) = 7 (9.61x + 9.3x2) = 7 Solving 9.61x + 9.3x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 9.61x + 9.3x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 9.61x + 9.3x2 = 0 Begin completing the square. Divide all terms by 9.3 the coefficient of the squared term: Divide each side by '9.3'. -0.752688172 + 1.033333333x + x2 = 0 Move the constant term to the right: Add '0.752688172' to each side of the equation. -0.752688172 + 1.033333333x + 0.752688172 + x2 = 0 + 0.752688172 Reorder the terms: -0.752688172 + 0.752688172 + 1.033333333x + x2 = 0 + 0.752688172 Combine like terms: -0.752688172 + 0.752688172 = 0.000000000 0.000000000 + 1.033333333x + x2 = 0 + 0.752688172 1.033333333x + x2 = 0 + 0.752688172 Combine like terms: 0 + 0.752688172 = 0.752688172 1.033333333x + x2 = 0.752688172 The x term is 1.033333333x. Take half its coefficient (0.5166666665). Square it (0.2669444443) and add it to both sides. Add '0.2669444443' to each side of the equation. 1.033333333x + 0.2669444443 + x2 = 0.752688172 + 0.2669444443 Reorder the terms: 0.2669444443 + 1.033333333x + x2 = 0.752688172 + 0.2669444443 Combine like terms: 0.752688172 + 0.2669444443 = 1.0196326163 0.2669444443 + 1.033333333x + x2 = 1.0196326163 Factor a perfect square on the left side: (x + 0.5166666665)(x + 0.5166666665) = 1.0196326163 Calculate the square root of the right side: 1.009768595 Break this problem into two subproblems by setting (x + 0.5166666665) equal to 1.009768595 and -1.009768595.Subproblem 1
x + 0.5166666665 = 1.009768595 Simplifying x + 0.5166666665 = 1.009768595 Reorder the terms: 0.5166666665 + x = 1.009768595 Solving 0.5166666665 + x = 1.009768595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5166666665' to each side of the equation. 0.5166666665 + -0.5166666665 + x = 1.009768595 + -0.5166666665 Combine like terms: 0.5166666665 + -0.5166666665 = 0.0000000000 0.0000000000 + x = 1.009768595 + -0.5166666665 x = 1.009768595 + -0.5166666665 Combine like terms: 1.009768595 + -0.5166666665 = 0.4931019285 x = 0.4931019285 Simplifying x = 0.4931019285Subproblem 2
x + 0.5166666665 = -1.009768595 Simplifying x + 0.5166666665 = -1.009768595 Reorder the terms: 0.5166666665 + x = -1.009768595 Solving 0.5166666665 + x = -1.009768595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5166666665' to each side of the equation. 0.5166666665 + -0.5166666665 + x = -1.009768595 + -0.5166666665 Combine like terms: 0.5166666665 + -0.5166666665 = 0.0000000000 0.0000000000 + x = -1.009768595 + -0.5166666665 x = -1.009768595 + -0.5166666665 Combine like terms: -1.009768595 + -0.5166666665 = -1.5264352615 x = -1.5264352615 Simplifying x = -1.5264352615Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4931019285, -1.5264352615}
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