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Simplifying 2x2 + 7x + -570 = 0 Reorder the terms: -570 + 7x + 2x2 = 0 Solving -570 + 7x + 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'. -285 + 3.5x + x2 = 0 Move the constant term to the right: Add '285' to each side of the equation. -285 + 3.5x + 285 + x2 = 0 + 285 Reorder the terms: -285 + 285 + 3.5x + x2 = 0 + 285 Combine like terms: -285 + 285 = 0 0 + 3.5x + x2 = 0 + 285 3.5x + x2 = 0 + 285 Combine like terms: 0 + 285 = 285 3.5x + x2 = 285 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 285 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 285 + 3.0625 Combine like terms: 285 + 3.0625 = 288.0625 3.0625 + 3.5x + x2 = 288.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 288.0625 Calculate the square root of the right side: 16.972404072 Break this problem into two subproblems by setting (x + 1.75) equal to 16.972404072 and -16.972404072.Subproblem 1
x + 1.75 = 16.972404072 Simplifying x + 1.75 = 16.972404072 Reorder the terms: 1.75 + x = 16.972404072 Solving 1.75 + x = 16.972404072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 16.972404072 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 16.972404072 + -1.75 x = 16.972404072 + -1.75 Combine like terms: 16.972404072 + -1.75 = 15.222404072 x = 15.222404072 Simplifying x = 15.222404072Subproblem 2
x + 1.75 = -16.972404072 Simplifying x + 1.75 = -16.972404072 Reorder the terms: 1.75 + x = -16.972404072 Solving 1.75 + x = -16.972404072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -16.972404072 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -16.972404072 + -1.75 x = -16.972404072 + -1.75 Combine like terms: -16.972404072 + -1.75 = -18.722404072 x = -18.722404072 Simplifying x = -18.722404072Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.222404072, -18.722404072}
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