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Simplifying 2x + 3 = 91x2 Reorder the terms: 3 + 2x = 91x2 Solving 3 + 2x = 91x2 Solving for variable 'x'. Combine like terms: 91x2 + -91x2 = 0 3 + 2x + -91x2 = 0 Begin completing the square. Divide all terms by -91 the coefficient of the squared term: Divide each side by '-91'. -0.03296703297 + -0.02197802198x + x2 = 0 Move the constant term to the right: Add '0.03296703297' to each side of the equation. -0.03296703297 + -0.02197802198x + 0.03296703297 + x2 = 0 + 0.03296703297 Reorder the terms: -0.03296703297 + 0.03296703297 + -0.02197802198x + x2 = 0 + 0.03296703297 Combine like terms: -0.03296703297 + 0.03296703297 = 0.00000000000 0.00000000000 + -0.02197802198x + x2 = 0 + 0.03296703297 -0.02197802198x + x2 = 0 + 0.03296703297 Combine like terms: 0 + 0.03296703297 = 0.03296703297 -0.02197802198x + x2 = 0.03296703297 The x term is -0.02197802198x. Take half its coefficient (-0.01098901099). Square it (0.0001207583625) and add it to both sides. Add '0.0001207583625' to each side of the equation. -0.02197802198x + 0.0001207583625 + x2 = 0.03296703297 + 0.0001207583625 Reorder the terms: 0.0001207583625 + -0.02197802198x + x2 = 0.03296703297 + 0.0001207583625 Combine like terms: 0.03296703297 + 0.0001207583625 = 0.0330877913325 0.0001207583625 + -0.02197802198x + x2 = 0.0330877913325 Factor a perfect square on the left side: (x + -0.01098901099)(x + -0.01098901099) = 0.0330877913325 Calculate the square root of the right side: 0.181900498 Break this problem into two subproblems by setting (x + -0.01098901099) equal to 0.181900498 and -0.181900498.Subproblem 1
x + -0.01098901099 = 0.181900498 Simplifying x + -0.01098901099 = 0.181900498 Reorder the terms: -0.01098901099 + x = 0.181900498 Solving -0.01098901099 + x = 0.181900498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01098901099' to each side of the equation. -0.01098901099 + 0.01098901099 + x = 0.181900498 + 0.01098901099 Combine like terms: -0.01098901099 + 0.01098901099 = 0.00000000000 0.00000000000 + x = 0.181900498 + 0.01098901099 x = 0.181900498 + 0.01098901099 Combine like terms: 0.181900498 + 0.01098901099 = 0.19288950899 x = 0.19288950899 Simplifying x = 0.19288950899Subproblem 2
x + -0.01098901099 = -0.181900498 Simplifying x + -0.01098901099 = -0.181900498 Reorder the terms: -0.01098901099 + x = -0.181900498 Solving -0.01098901099 + x = -0.181900498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01098901099' to each side of the equation. -0.01098901099 + 0.01098901099 + x = -0.181900498 + 0.01098901099 Combine like terms: -0.01098901099 + 0.01098901099 = 0.00000000000 0.00000000000 + x = -0.181900498 + 0.01098901099 x = -0.181900498 + 0.01098901099 Combine like terms: -0.181900498 + 0.01098901099 = -0.17091148701 x = -0.17091148701 Simplifying x = -0.17091148701Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.19288950899, -0.17091148701}
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