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Simplifying (3x2) + 90x + -1 = 0 Reorder the terms: -1 + 90x + (3x2) = 0 Solving -1 + 90x + (3x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 30x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 30x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 30x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 30x + x2 = 0 + 0.3333333333 30x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 30x + x2 = 0.3333333333 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 0.3333333333 + 225 Reorder the terms: 225 + 30x + x2 = 0.3333333333 + 225 Combine like terms: 0.3333333333 + 225 = 225.3333333333 225 + 30x + x2 = 225.3333333333 Factor a perfect square on the left side: ((x) + 15)((x) + 15) = 225.3333333333 Calculate the square root of the right side: 15.011106999 Break this problem into two subproblems by setting ((x) + 15) equal to 15.011106999 and -15.011106999.Subproblem 1
(x) + 15 = 15.011106999 Simplifying (x) + 15 = 15.011106999 x + 15 = 15.011106999 Reorder the terms: 15 + x = 15.011106999 Solving 15 + x = 15.011106999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 15.011106999 + -15 Combine like terms: 15 + -15 = 0 0 + x = 15.011106999 + -15 x = 15.011106999 + -15 Combine like terms: 15.011106999 + -15 = 0.011106999 x = 0.011106999 Simplifying x = 0.011106999Subproblem 2
(x) + 15 = -15.011106999 Simplifying (x) + 15 = -15.011106999 x + 15 = -15.011106999 Reorder the terms: 15 + x = -15.011106999 Solving 15 + x = -15.011106999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -15.011106999 + -15 Combine like terms: 15 + -15 = 0 0 + x = -15.011106999 + -15 x = -15.011106999 + -15 Combine like terms: -15.011106999 + -15 = -30.011106999 x = -30.011106999 Simplifying x = -30.011106999Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.011106999, -30.011106999}
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