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Simplifying (15x * 15x) + 5x + -3x + -1 = 0 Reorder the terms for easier multiplication: (15 * 15x * x) + 5x + -3x + -1 = 0 Multiply 15 * 15 (225x * x) + 5x + -3x + -1 = 0 Multiply x * x (225x2) + 5x + -3x + -1 = 0 Reorder the terms: -1 + 5x + -3x + (225x2) = 0 Combine like terms: 5x + -3x = 2x -1 + 2x + (225x2) = 0 Solving -1 + 2x + (225x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 225 the coefficient of the squared term: Divide each side by '225'. -0.004444444444 + 0.008888888889x + x2 = 0 Move the constant term to the right: Add '0.004444444444' to each side of the equation. -0.004444444444 + 0.008888888889x + 0.004444444444 + x2 = 0 + 0.004444444444 Reorder the terms: -0.004444444444 + 0.004444444444 + 0.008888888889x + x2 = 0 + 0.004444444444 Combine like terms: -0.004444444444 + 0.004444444444 = 0.000000000000 0.000000000000 + 0.008888888889x + x2 = 0 + 0.004444444444 0.008888888889x + x2 = 0 + 0.004444444444 Combine like terms: 0 + 0.004444444444 = 0.004444444444 0.008888888889x + x2 = 0.004444444444 The x term is 0.008888888889x. Take half its coefficient (0.004444444445). Square it (0.00001975308642) and add it to both sides. Add '0.00001975308642' to each side of the equation. 0.008888888889x + 0.00001975308642 + x2 = 0.004444444444 + 0.00001975308642 Reorder the terms: 0.00001975308642 + 0.008888888889x + x2 = 0.004444444444 + 0.00001975308642 Combine like terms: 0.004444444444 + 0.00001975308642 = 0.00446419753042 0.00001975308642 + 0.008888888889x + x2 = 0.00446419753042 Factor a perfect square on the left side: ((x) + 0.004444444445)((x) + 0.004444444445) = 0.00446419753042 Calculate the square root of the right side: 0.066814651 Break this problem into two subproblems by setting ((x) + 0.004444444445) equal to 0.066814651 and -0.066814651.Subproblem 1
(x) + 0.004444444445 = 0.066814651 Simplifying (x) + 0.004444444445 = 0.066814651 x + 0.004444444445 = 0.066814651 Reorder the terms: 0.004444444445 + x = 0.066814651 Solving 0.004444444445 + x = 0.066814651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.004444444445' to each side of the equation. 0.004444444445 + -0.004444444445 + x = 0.066814651 + -0.004444444445 Combine like terms: 0.004444444445 + -0.004444444445 = 0.000000000000 0.000000000000 + x = 0.066814651 + -0.004444444445 x = 0.066814651 + -0.004444444445 Combine like terms: 0.066814651 + -0.004444444445 = 0.062370206555 x = 0.062370206555 Simplifying x = 0.062370206555Subproblem 2
(x) + 0.004444444445 = -0.066814651 Simplifying (x) + 0.004444444445 = -0.066814651 x + 0.004444444445 = -0.066814651 Reorder the terms: 0.004444444445 + x = -0.066814651 Solving 0.004444444445 + x = -0.066814651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.004444444445' to each side of the equation. 0.004444444445 + -0.004444444445 + x = -0.066814651 + -0.004444444445 Combine like terms: 0.004444444445 + -0.004444444445 = 0.000000000000 0.000000000000 + x = -0.066814651 + -0.004444444445 x = -0.066814651 + -0.004444444445 Combine like terms: -0.066814651 + -0.004444444445 = -0.071259095445 x = -0.071259095445 Simplifying x = -0.071259095445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.062370206555, -0.071259095445}
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