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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 = 27.66666667 16 + -8x + x2 = 27.66666667 Factor a perfect square on the left side: ((x) + -4)((x) + -4) = 27.66666667 Calculate the square root of the right side: 5.25991128 Break this problem into two subproblems by setting ((x) + -4) equal to 5.25991128 and -5.25991128.Subproblem 1
(x) + -4 = 5.25991128 Simplifying (x) + -4 = 5.25991128 x + -4 = 5.25991128 Reorder the terms: -4 + x = 5.25991128 Solving -4 + x = 5.25991128 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 = 5.25991128 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.25991128 + 4 x = 5.25991128 + 4 Combine like terms: 5.25991128 + 4 = 9.25991128 x = 9.25991128 Simplifying x = 9.25991128Subproblem 2
(x) + -4 = -5.25991128 Simplifying (x) + -4 = -5.25991128 x + -4 = -5.25991128 Reorder the terms: -4 + x = -5.25991128 Solving -4 + x = -5.25991128 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 = -5.25991128 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.25991128 + 4 x = -5.25991128 + 4 Combine like terms: -5.25991128 + 4 = -1.25991128 x = -1.25991128 Simplifying x = -1.25991128Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.25991128, -1.25991128}
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