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Simplifying x(13x + 7) = 30 Reorder the terms: x(7 + 13x) = 30 (7 * x + 13x * x) = 30 (7x + 13x2) = 30 Solving 7x + 13x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 7x + 13x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 7x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -2.307692308 + 0.5384615385x + x2 = 0 Move the constant term to the right: Add '2.307692308' to each side of the equation. -2.307692308 + 0.5384615385x + 2.307692308 + x2 = 0 + 2.307692308 Reorder the terms: -2.307692308 + 2.307692308 + 0.5384615385x + x2 = 0 + 2.307692308 Combine like terms: -2.307692308 + 2.307692308 = 0.000000000 0.000000000 + 0.5384615385x + x2 = 0 + 2.307692308 0.5384615385x + x2 = 0 + 2.307692308 Combine like terms: 0 + 2.307692308 = 2.307692308 0.5384615385x + x2 = 2.307692308 The x term is 0.5384615385x. Take half its coefficient (0.2692307693). Square it (0.07248520714) and add it to both sides. Add '0.07248520714' to each side of the equation. 0.5384615385x + 0.07248520714 + x2 = 2.307692308 + 0.07248520714 Reorder the terms: 0.07248520714 + 0.5384615385x + x2 = 2.307692308 + 0.07248520714 Combine like terms: 2.307692308 + 0.07248520714 = 2.38017751514 0.07248520714 + 0.5384615385x + x2 = 2.38017751514 Factor a perfect square on the left side: (x + 0.2692307693)(x + 0.2692307693) = 2.38017751514 Calculate the square root of the right side: 1.542782394 Break this problem into two subproblems by setting (x + 0.2692307693) equal to 1.542782394 and -1.542782394.Subproblem 1
x + 0.2692307693 = 1.542782394 Simplifying x + 0.2692307693 = 1.542782394 Reorder the terms: 0.2692307693 + x = 1.542782394 Solving 0.2692307693 + x = 1.542782394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = 1.542782394 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = 1.542782394 + -0.2692307693 x = 1.542782394 + -0.2692307693 Combine like terms: 1.542782394 + -0.2692307693 = 1.2735516247 x = 1.2735516247 Simplifying x = 1.2735516247Subproblem 2
x + 0.2692307693 = -1.542782394 Simplifying x + 0.2692307693 = -1.542782394 Reorder the terms: 0.2692307693 + x = -1.542782394 Solving 0.2692307693 + x = -1.542782394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = -1.542782394 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = -1.542782394 + -0.2692307693 x = -1.542782394 + -0.2692307693 Combine like terms: -1.542782394 + -0.2692307693 = -1.8120131633 x = -1.8120131633 Simplifying x = -1.8120131633Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2735516247, -1.8120131633}
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