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Simplifying 2x2 + 2x + -287 = 0 Reorder the terms: -287 + 2x + 2x2 = 0 Solving -287 + 2x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -143.5 + x + x2 = 0 Move the constant term to the right: Add '143.5' to each side of the equation. -143.5 + x + 143.5 + x2 = 0 + 143.5 Reorder the terms: -143.5 + 143.5 + x + x2 = 0 + 143.5 Combine like terms: -143.5 + 143.5 = 0.0 0.0 + x + x2 = 0 + 143.5 x + x2 = 0 + 143.5 Combine like terms: 0 + 143.5 = 143.5 x + x2 = 143.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 143.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 143.5 + 0.25 Combine like terms: 143.5 + 0.25 = 143.75 1.25 + x2 = 143.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 143.75 Calculate the square root of the right side: 11.989578808 Break this problem into two subproblems by setting (x + 0.5) equal to 11.989578808 and -11.989578808.Subproblem 1
x + 0.5 = 11.989578808 Simplifying x + 0.5 = 11.989578808 Reorder the terms: 0.5 + x = 11.989578808 Solving 0.5 + x = 11.989578808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 11.989578808 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.989578808 + -0.5 x = 11.989578808 + -0.5 Combine like terms: 11.989578808 + -0.5 = 11.489578808 x = 11.489578808 Simplifying x = 11.489578808Subproblem 2
x + 0.5 = -11.989578808 Simplifying x + 0.5 = -11.989578808 Reorder the terms: 0.5 + x = -11.989578808 Solving 0.5 + x = -11.989578808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -11.989578808 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.989578808 + -0.5 x = -11.989578808 + -0.5 Combine like terms: -11.989578808 + -0.5 = -12.489578808 x = -12.489578808 Simplifying x = -12.489578808Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.489578808, -12.489578808}
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