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Simplifying 3x2 + -24x + 35 = 0 Reorder the terms: 35 + -24x + 3x2 = 0 Solving 35 + -24x + 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'. 11.66666667 + -8x + x2 = 0 Move the constant term to the right: Add '-11.66666667' to each side of the equation. 11.66666667 + -8x + -11.66666667 + x2 = 0 + -11.66666667 Reorder the terms: 11.66666667 + -11.66666667 + -8x + x2 = 0 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + -8x + x2 = 0 + -11.66666667 -8x + x2 = 0 + -11.66666667 Combine like terms: 0 + -11.66666667 = -11.66666667 -8x + x2 = -11.66666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -11.66666667 + 16 Reorder the terms: 16 + -8x + x2 = -11.66666667 + 16 Combine like terms: -11.66666667 + 16 = 4.33333333 16 + -8x + x2 = 4.33333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 4.33333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (x + -4) equal to 2.081665999 and -2.081665999.Subproblem 1
x + -4 = 2.081665999 Simplifying x + -4 = 2.081665999 Reorder the terms: -4 + x = 2.081665999 Solving -4 + x = 2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.081665999 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.081665999 + 4 x = 2.081665999 + 4 Combine like terms: 2.081665999 + 4 = 6.081665999 x = 6.081665999 Simplifying x = 6.081665999Subproblem 2
x + -4 = -2.081665999 Simplifying x + -4 = -2.081665999 Reorder the terms: -4 + x = -2.081665999 Solving -4 + x = -2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.081665999 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.081665999 + 4 x = -2.081665999 + 4 Combine like terms: -2.081665999 + 4 = 1.918334001 x = 1.918334001 Simplifying x = 1.918334001Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.081665999, 1.918334001}
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