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Simplifying 3x2 + -90x + 128 = 0 Reorder the terms: 128 + -90x + 3x2 = 0 Solving 128 + -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'. 42.66666667 + -30x + x2 = 0 Move the constant term to the right: Add '-42.66666667' to each side of the equation. 42.66666667 + -30x + -42.66666667 + x2 = 0 + -42.66666667 Reorder the terms: 42.66666667 + -42.66666667 + -30x + x2 = 0 + -42.66666667 Combine like terms: 42.66666667 + -42.66666667 = 0.00000000 0.00000000 + -30x + x2 = 0 + -42.66666667 -30x + x2 = 0 + -42.66666667 Combine like terms: 0 + -42.66666667 = -42.66666667 -30x + x2 = -42.66666667 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 = -42.66666667 + 225 Reorder the terms: 225 + -30x + x2 = -42.66666667 + 225 Combine like terms: -42.66666667 + 225 = 182.33333333 225 + -30x + x2 = 182.33333333 Factor a perfect square on the left side: (x + -15)(x + -15) = 182.33333333 Calculate the square root of the right side: 13.503086067 Break this problem into two subproblems by setting (x + -15) equal to 13.503086067 and -13.503086067.Subproblem 1
x + -15 = 13.503086067 Simplifying x + -15 = 13.503086067 Reorder the terms: -15 + x = 13.503086067 Solving -15 + x = 13.503086067 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 = 13.503086067 + 15 Combine like terms: -15 + 15 = 0 0 + x = 13.503086067 + 15 x = 13.503086067 + 15 Combine like terms: 13.503086067 + 15 = 28.503086067 x = 28.503086067 Simplifying x = 28.503086067Subproblem 2
x + -15 = -13.503086067 Simplifying x + -15 = -13.503086067 Reorder the terms: -15 + x = -13.503086067 Solving -15 + x = -13.503086067 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 = -13.503086067 + 15 Combine like terms: -15 + 15 = 0 0 + x = -13.503086067 + 15 x = -13.503086067 + 15 Combine like terms: -13.503086067 + 15 = 1.496913933 x = 1.496913933 Simplifying x = 1.496913933Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.503086067, 1.496913933}
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