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Simplifying 97 = 5x2 + 7x Reorder the terms: 97 = 7x + 5x2 Solving 97 = 7x + 5x2 Solving for variable 'x'. Reorder the terms: 97 + -7x + -5x2 = 7x + -7x + 5x2 + -5x2 Combine like terms: 7x + -7x = 0 97 + -7x + -5x2 = 0 + 5x2 + -5x2 97 + -7x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 97 + -7x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -19.4 + 1.4x + x2 = 0 Move the constant term to the right: Add '19.4' to each side of the equation. -19.4 + 1.4x + 19.4 + x2 = 0 + 19.4 Reorder the terms: -19.4 + 19.4 + 1.4x + x2 = 0 + 19.4 Combine like terms: -19.4 + 19.4 = 0.0 0.0 + 1.4x + x2 = 0 + 19.4 1.4x + x2 = 0 + 19.4 Combine like terms: 0 + 19.4 = 19.4 1.4x + x2 = 19.4 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 19.4 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 19.4 + 0.49 Combine like terms: 19.4 + 0.49 = 19.89 0.49 + 1.4x + x2 = 19.89 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 19.89 Calculate the square root of the right side: 4.459820624 Break this problem into two subproblems by setting (x + 0.7) equal to 4.459820624 and -4.459820624.Subproblem 1
x + 0.7 = 4.459820624 Simplifying x + 0.7 = 4.459820624 Reorder the terms: 0.7 + x = 4.459820624 Solving 0.7 + x = 4.459820624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 4.459820624 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 4.459820624 + -0.7 x = 4.459820624 + -0.7 Combine like terms: 4.459820624 + -0.7 = 3.759820624 x = 3.759820624 Simplifying x = 3.759820624Subproblem 2
x + 0.7 = -4.459820624 Simplifying x + 0.7 = -4.459820624 Reorder the terms: 0.7 + x = -4.459820624 Solving 0.7 + x = -4.459820624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -4.459820624 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -4.459820624 + -0.7 x = -4.459820624 + -0.7 Combine like terms: -4.459820624 + -0.7 = -5.159820624 x = -5.159820624 Simplifying x = -5.159820624Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.759820624, -5.159820624}
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