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Simplifying -5.2x2 + 24x + -0.764 = 0 Reorder the terms: -0.764 + 24x + -5.2x2 = 0 Solving -0.764 + 24x + -5.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5.2 the coefficient of the squared term: Divide each side by '-5.2'. 0.1469230769 + -4.615384615x + x2 = 0 Move the constant term to the right: Add '-0.1469230769' to each side of the equation. 0.1469230769 + -4.615384615x + -0.1469230769 + x2 = 0 + -0.1469230769 Reorder the terms: 0.1469230769 + -0.1469230769 + -4.615384615x + x2 = 0 + -0.1469230769 Combine like terms: 0.1469230769 + -0.1469230769 = 0.0000000000 0.0000000000 + -4.615384615x + x2 = 0 + -0.1469230769 -4.615384615x + x2 = 0 + -0.1469230769 Combine like terms: 0 + -0.1469230769 = -0.1469230769 -4.615384615x + x2 = -0.1469230769 The x term is -4.615384615x. Take half its coefficient (-2.307692308). Square it (5.325443788) and add it to both sides. Add '5.325443788' to each side of the equation. -4.615384615x + 5.325443788 + x2 = -0.1469230769 + 5.325443788 Reorder the terms: 5.325443788 + -4.615384615x + x2 = -0.1469230769 + 5.325443788 Combine like terms: -0.1469230769 + 5.325443788 = 5.1785207111 5.325443788 + -4.615384615x + x2 = 5.1785207111 Factor a perfect square on the left side: (x + -2.307692308)(x + -2.307692308) = 5.1785207111 Calculate the square root of the right side: 2.275636331 Break this problem into two subproblems by setting (x + -2.307692308) equal to 2.275636331 and -2.275636331.Subproblem 1
x + -2.307692308 = 2.275636331 Simplifying x + -2.307692308 = 2.275636331 Reorder the terms: -2.307692308 + x = 2.275636331 Solving -2.307692308 + x = 2.275636331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.307692308' to each side of the equation. -2.307692308 + 2.307692308 + x = 2.275636331 + 2.307692308 Combine like terms: -2.307692308 + 2.307692308 = 0.000000000 0.000000000 + x = 2.275636331 + 2.307692308 x = 2.275636331 + 2.307692308 Combine like terms: 2.275636331 + 2.307692308 = 4.583328639 x = 4.583328639 Simplifying x = 4.583328639Subproblem 2
x + -2.307692308 = -2.275636331 Simplifying x + -2.307692308 = -2.275636331 Reorder the terms: -2.307692308 + x = -2.275636331 Solving -2.307692308 + x = -2.275636331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.307692308' to each side of the equation. -2.307692308 + 2.307692308 + x = -2.275636331 + 2.307692308 Combine like terms: -2.307692308 + 2.307692308 = 0.000000000 0.000000000 + x = -2.275636331 + 2.307692308 x = -2.275636331 + 2.307692308 Combine like terms: -2.275636331 + 2.307692308 = 0.032055977 x = 0.032055977 Simplifying x = 0.032055977Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.583328639, 0.032055977}
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