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Simplifying 5x2 + -43x + -7 = 0 Reorder the terms: -7 + -43x + 5x2 = 0 Solving -7 + -43x + 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'. -1.4 + -8.6x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -8.6x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -8.6x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -8.6x + x2 = 0 + 1.4 -8.6x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -8.6x + x2 = 1.4 The x term is -8.6x. Take half its coefficient (-4.3). Square it (18.49) and add it to both sides. Add '18.49' to each side of the equation. -8.6x + 18.49 + x2 = 1.4 + 18.49 Reorder the terms: 18.49 + -8.6x + x2 = 1.4 + 18.49 Combine like terms: 1.4 + 18.49 = 19.89 18.49 + -8.6x + x2 = 19.89 Factor a perfect square on the left side: (x + -4.3)(x + -4.3) = 19.89 Calculate the square root of the right side: 4.459820624 Break this problem into two subproblems by setting (x + -4.3) equal to 4.459820624 and -4.459820624.Subproblem 1
x + -4.3 = 4.459820624 Simplifying x + -4.3 = 4.459820624 Reorder the terms: -4.3 + x = 4.459820624 Solving -4.3 + x = 4.459820624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.3' to each side of the equation. -4.3 + 4.3 + x = 4.459820624 + 4.3 Combine like terms: -4.3 + 4.3 = 0.0 0.0 + x = 4.459820624 + 4.3 x = 4.459820624 + 4.3 Combine like terms: 4.459820624 + 4.3 = 8.759820624 x = 8.759820624 Simplifying x = 8.759820624Subproblem 2
x + -4.3 = -4.459820624 Simplifying x + -4.3 = -4.459820624 Reorder the terms: -4.3 + x = -4.459820624 Solving -4.3 + x = -4.459820624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.3' to each side of the equation. -4.3 + 4.3 + x = -4.459820624 + 4.3 Combine like terms: -4.3 + 4.3 = 0.0 0.0 + x = -4.459820624 + 4.3 x = -4.459820624 + 4.3 Combine like terms: -4.459820624 + 4.3 = -0.159820624 x = -0.159820624 Simplifying x = -0.159820624Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.759820624, -0.159820624}
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