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Simplifying 5x2 + -8x + -675 = 0 Reorder the terms: -675 + -8x + 5x2 = 0 Solving -675 + -8x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -135 + -1.6x + x2 = 0 Move the constant term to the right: Add '135' to each side of the equation. -135 + -1.6x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + -1.6x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + -1.6x + x2 = 0 + 135 -1.6x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 -1.6x + x2 = 135 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 135 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 135 + 0.64 Combine like terms: 135 + 0.64 = 135.64 0.64 + -1.6x + x2 = 135.64 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 135.64 Calculate the square root of the right side: 11.646458689 Break this problem into two subproblems by setting (x + -0.8) equal to 11.646458689 and -11.646458689.Subproblem 1
x + -0.8 = 11.646458689 Simplifying x + -0.8 = 11.646458689 Reorder the terms: -0.8 + x = 11.646458689 Solving -0.8 + x = 11.646458689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 11.646458689 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 11.646458689 + 0.8 x = 11.646458689 + 0.8 Combine like terms: 11.646458689 + 0.8 = 12.446458689 x = 12.446458689 Simplifying x = 12.446458689Subproblem 2
x + -0.8 = -11.646458689 Simplifying x + -0.8 = -11.646458689 Reorder the terms: -0.8 + x = -11.646458689 Solving -0.8 + x = -11.646458689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -11.646458689 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -11.646458689 + 0.8 x = -11.646458689 + 0.8 Combine like terms: -11.646458689 + 0.8 = -10.846458689 x = -10.846458689 Simplifying x = -10.846458689Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.446458689, -10.846458689}
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