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Simplifying 6.99x2 + 2.75x + -5.29 = 0 Reorder the terms: -5.29 + 2.75x + 6.99x2 = 0 Solving -5.29 + 2.75x + 6.99x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.99 the coefficient of the squared term: Divide each side by '6.99'. -0.756795422 + 0.3934191702x + x2 = 0 Move the constant term to the right: Add '0.756795422' to each side of the equation. -0.756795422 + 0.3934191702x + 0.756795422 + x2 = 0 + 0.756795422 Reorder the terms: -0.756795422 + 0.756795422 + 0.3934191702x + x2 = 0 + 0.756795422 Combine like terms: -0.756795422 + 0.756795422 = 0.000000000 0.000000000 + 0.3934191702x + x2 = 0 + 0.756795422 0.3934191702x + x2 = 0 + 0.756795422 Combine like terms: 0 + 0.756795422 = 0.756795422 0.3934191702x + x2 = 0.756795422 The x term is 0.3934191702x. Take half its coefficient (0.1967095851). Square it (0.03869466087) and add it to both sides. Add '0.03869466087' to each side of the equation. 0.3934191702x + 0.03869466087 + x2 = 0.756795422 + 0.03869466087 Reorder the terms: 0.03869466087 + 0.3934191702x + x2 = 0.756795422 + 0.03869466087 Combine like terms: 0.756795422 + 0.03869466087 = 0.79549008287 0.03869466087 + 0.3934191702x + x2 = 0.79549008287 Factor a perfect square on the left side: (x + 0.1967095851)(x + 0.1967095851) = 0.79549008287 Calculate the square root of the right side: 0.891902507 Break this problem into two subproblems by setting (x + 0.1967095851) equal to 0.891902507 and -0.891902507.Subproblem 1
x + 0.1967095851 = 0.891902507 Simplifying x + 0.1967095851 = 0.891902507 Reorder the terms: 0.1967095851 + x = 0.891902507 Solving 0.1967095851 + x = 0.891902507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1967095851' to each side of the equation. 0.1967095851 + -0.1967095851 + x = 0.891902507 + -0.1967095851 Combine like terms: 0.1967095851 + -0.1967095851 = 0.0000000000 0.0000000000 + x = 0.891902507 + -0.1967095851 x = 0.891902507 + -0.1967095851 Combine like terms: 0.891902507 + -0.1967095851 = 0.6951929219 x = 0.6951929219 Simplifying x = 0.6951929219Subproblem 2
x + 0.1967095851 = -0.891902507 Simplifying x + 0.1967095851 = -0.891902507 Reorder the terms: 0.1967095851 + x = -0.891902507 Solving 0.1967095851 + x = -0.891902507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1967095851' to each side of the equation. 0.1967095851 + -0.1967095851 + x = -0.891902507 + -0.1967095851 Combine like terms: 0.1967095851 + -0.1967095851 = 0.0000000000 0.0000000000 + x = -0.891902507 + -0.1967095851 x = -0.891902507 + -0.1967095851 Combine like terms: -0.891902507 + -0.1967095851 = -1.0886120921 x = -1.0886120921 Simplifying x = -1.0886120921Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6951929219, -1.0886120921}
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