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Simplifying 5x2 + -8x + -43 = 0 Reorder the terms: -43 + -8x + 5x2 = 0 Solving -43 + -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'. -8.6 + -1.6x + x2 = 0 Move the constant term to the right: Add '8.6' to each side of the equation. -8.6 + -1.6x + 8.6 + x2 = 0 + 8.6 Reorder the terms: -8.6 + 8.6 + -1.6x + x2 = 0 + 8.6 Combine like terms: -8.6 + 8.6 = 0.0 0.0 + -1.6x + x2 = 0 + 8.6 -1.6x + x2 = 0 + 8.6 Combine like terms: 0 + 8.6 = 8.6 -1.6x + x2 = 8.6 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 = 8.6 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 8.6 + 0.64 Combine like terms: 8.6 + 0.64 = 9.24 0.64 + -1.6x + x2 = 9.24 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 9.24 Calculate the square root of the right side: 3.039736831 Break this problem into two subproblems by setting (x + -0.8) equal to 3.039736831 and -3.039736831.Subproblem 1
x + -0.8 = 3.039736831 Simplifying x + -0.8 = 3.039736831 Reorder the terms: -0.8 + x = 3.039736831 Solving -0.8 + x = 3.039736831 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 = 3.039736831 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 3.039736831 + 0.8 x = 3.039736831 + 0.8 Combine like terms: 3.039736831 + 0.8 = 3.839736831 x = 3.839736831 Simplifying x = 3.839736831Subproblem 2
x + -0.8 = -3.039736831 Simplifying x + -0.8 = -3.039736831 Reorder the terms: -0.8 + x = -3.039736831 Solving -0.8 + x = -3.039736831 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 = -3.039736831 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -3.039736831 + 0.8 x = -3.039736831 + 0.8 Combine like terms: -3.039736831 + 0.8 = -2.239736831 x = -2.239736831 Simplifying x = -2.239736831Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.839736831, -2.239736831}
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