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Simplifying 5x2 + -97x + -38 = 0 Reorder the terms: -38 + -97x + 5x2 = 0 Solving -38 + -97x + 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'. -7.6 + -19.4x + x2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + -19.4x + 7.6 + x2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + -19.4x + x2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + -19.4x + x2 = 0 + 7.6 -19.4x + x2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 -19.4x + x2 = 7.6 The x term is -19.4x. Take half its coefficient (-9.7). Square it (94.09) and add it to both sides. Add '94.09' to each side of the equation. -19.4x + 94.09 + x2 = 7.6 + 94.09 Reorder the terms: 94.09 + -19.4x + x2 = 7.6 + 94.09 Combine like terms: 7.6 + 94.09 = 101.69 94.09 + -19.4x + x2 = 101.69 Factor a perfect square on the left side: (x + -9.7)(x + -9.7) = 101.69 Calculate the square root of the right side: 10.084145973 Break this problem into two subproblems by setting (x + -9.7) equal to 10.084145973 and -10.084145973.Subproblem 1
x + -9.7 = 10.084145973 Simplifying x + -9.7 = 10.084145973 Reorder the terms: -9.7 + x = 10.084145973 Solving -9.7 + x = 10.084145973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.7' to each side of the equation. -9.7 + 9.7 + x = 10.084145973 + 9.7 Combine like terms: -9.7 + 9.7 = 0.0 0.0 + x = 10.084145973 + 9.7 x = 10.084145973 + 9.7 Combine like terms: 10.084145973 + 9.7 = 19.784145973 x = 19.784145973 Simplifying x = 19.784145973Subproblem 2
x + -9.7 = -10.084145973 Simplifying x + -9.7 = -10.084145973 Reorder the terms: -9.7 + x = -10.084145973 Solving -9.7 + x = -10.084145973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.7' to each side of the equation. -9.7 + 9.7 + x = -10.084145973 + 9.7 Combine like terms: -9.7 + 9.7 = 0.0 0.0 + x = -10.084145973 + 9.7 x = -10.084145973 + 9.7 Combine like terms: -10.084145973 + 9.7 = -0.384145973 x = -0.384145973 Simplifying x = -0.384145973Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.784145973, -0.384145973}
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