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Simplifying 3x(3x + -1) = x2 + 20 Reorder the terms: 3x(-1 + 3x) = x2 + 20 (-1 * 3x + 3x * 3x) = x2 + 20 (-3x + 9x2) = x2 + 20 Reorder the terms: -3x + 9x2 = 20 + x2 Solving -3x + 9x2 = 20 + x2 Solving for variable 'x'. Reorder the terms: -20 + -3x + 9x2 + -1x2 = 20 + x2 + -20 + -1x2 Combine like terms: 9x2 + -1x2 = 8x2 -20 + -3x + 8x2 = 20 + x2 + -20 + -1x2 Reorder the terms: -20 + -3x + 8x2 = 20 + -20 + x2 + -1x2 Combine like terms: 20 + -20 = 0 -20 + -3x + 8x2 = 0 + x2 + -1x2 -20 + -3x + 8x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -20 + -3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.5 + -0.375x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.375x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.375x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.375x + x2 = 0 + 2.5 -0.375x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.375x + x2 = 2.5 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 2.5 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 2.5 + 0.03515625 Combine like terms: 2.5 + 0.03515625 = 2.53515625 0.03515625 + -0.375x + x2 = 2.53515625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 2.53515625 Calculate the square root of the right side: 1.5922174 Break this problem into two subproblems by setting (x + -0.1875) equal to 1.5922174 and -1.5922174.Subproblem 1
x + -0.1875 = 1.5922174 Simplifying x + -0.1875 = 1.5922174 Reorder the terms: -0.1875 + x = 1.5922174 Solving -0.1875 + x = 1.5922174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 1.5922174 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 1.5922174 + 0.1875 x = 1.5922174 + 0.1875 Combine like terms: 1.5922174 + 0.1875 = 1.7797174 x = 1.7797174 Simplifying x = 1.7797174Subproblem 2
x + -0.1875 = -1.5922174 Simplifying x + -0.1875 = -1.5922174 Reorder the terms: -0.1875 + x = -1.5922174 Solving -0.1875 + x = -1.5922174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -1.5922174 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -1.5922174 + 0.1875 x = -1.5922174 + 0.1875 Combine like terms: -1.5922174 + 0.1875 = -1.4047174 x = -1.4047174 Simplifying x = -1.4047174Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7797174, -1.4047174}
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