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Simplifying 4.9x2 + -5x = 11.025 Reorder the terms: -5x + 4.9x2 = 11.025 Solving -5x + 4.9x2 = 11.025 Solving for variable 'x'. Reorder the terms: -11.025 + -5x + 4.9x2 = 11.025 + -11.025 Combine like terms: 11.025 + -11.025 = 0.000 -11.025 + -5x + 4.9x2 = 0.000 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -2.25 + -1.020408163x + x2 = 0.00 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1.020408163x + 2.25 + x2 = 0.00 + 2.25 Reorder the terms: -2.25 + 2.25 + -1.020408163x + x2 = 0.00 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1.020408163x + x2 = 0.00 + 2.25 -1.020408163x + x2 = 0.00 + 2.25 Combine like terms: 0.00 + 2.25 = 2.25 -1.020408163x + x2 = 2.25 The x term is -1.020408163x. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163x + 0.2603082048 + x2 = 2.25 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163x + x2 = 2.25 + 0.2603082048 Combine like terms: 2.25 + 0.2603082048 = 2.5103082048 0.2603082048 + -1.020408163x + x2 = 2.5103082048 Factor a perfect square on the left side: (x + -0.5102040815)(x + -0.5102040815) = 2.5103082048 Calculate the square root of the right side: 1.584395217 Break this problem into two subproblems by setting (x + -0.5102040815) equal to 1.584395217 and -1.584395217.Subproblem 1
x + -0.5102040815 = 1.584395217 Simplifying x + -0.5102040815 = 1.584395217 Reorder the terms: -0.5102040815 + x = 1.584395217 Solving -0.5102040815 + x = 1.584395217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = 1.584395217 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = 1.584395217 + 0.5102040815 x = 1.584395217 + 0.5102040815 Combine like terms: 1.584395217 + 0.5102040815 = 2.0945992985 x = 2.0945992985 Simplifying x = 2.0945992985Subproblem 2
x + -0.5102040815 = -1.584395217 Simplifying x + -0.5102040815 = -1.584395217 Reorder the terms: -0.5102040815 + x = -1.584395217 Solving -0.5102040815 + x = -1.584395217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = -1.584395217 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = -1.584395217 + 0.5102040815 x = -1.584395217 + 0.5102040815 Combine like terms: -1.584395217 + 0.5102040815 = -1.0741911355 x = -1.0741911355 Simplifying x = -1.0741911355Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0945992985, -1.0741911355}
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