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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 = 224.6666666667 225 + -30x + x2 = 224.6666666667 Factor a perfect square on the left side: ((x) + -15)((x) + -15) = 224.6666666667 Calculate the square root of the right side: 14.988884771 Break this problem into two subproblems by setting ((x) + -15) equal to 14.988884771 and -14.988884771.Subproblem 1
(x) + -15 = 14.988884771 Simplifying (x) + -15 = 14.988884771 x + -15 = 14.988884771 Reorder the terms: -15 + x = 14.988884771 Solving -15 + x = 14.988884771 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 = 14.988884771 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.988884771 + 15 x = 14.988884771 + 15 Combine like terms: 14.988884771 + 15 = 29.988884771 x = 29.988884771 Simplifying x = 29.988884771Subproblem 2
(x) + -15 = -14.988884771 Simplifying (x) + -15 = -14.988884771 x + -15 = -14.988884771 Reorder the terms: -15 + x = -14.988884771 Solving -15 + x = -14.988884771 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 = -14.988884771 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.988884771 + 15 x = -14.988884771 + 15 Combine like terms: -14.988884771 + 15 = 0.011115229 x = 0.011115229 Simplifying x = 0.011115229Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.988884771, 0.011115229}
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