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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 = 1.0741911355 x = 1.0741911355 Simplifying x = 1.0741911355Subproblem 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 = -2.0945992985 x = -2.0945992985 Simplifying x = -2.0945992985Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0741911355, -2.0945992985}
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