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Simplifying -0.06x2 = 9.6x + 5.4 Reorder the terms: -0.06x2 = 5.4 + 9.6x Solving -0.06x2 = 5.4 + 9.6x Solving for variable 'x'. Reorder the terms: -5.4 + -9.6x + -0.06x2 = 5.4 + 9.6x + -5.4 + -9.6x Reorder the terms: -5.4 + -9.6x + -0.06x2 = 5.4 + -5.4 + 9.6x + -9.6x Combine like terms: 5.4 + -5.4 = 0.0 -5.4 + -9.6x + -0.06x2 = 0.0 + 9.6x + -9.6x -5.4 + -9.6x + -0.06x2 = 9.6x + -9.6x Combine like terms: 9.6x + -9.6x = 0.0 -5.4 + -9.6x + -0.06x2 = 0.0 Begin completing the square. Divide all terms by -0.06 the coefficient of the squared term: Divide each side by '-0.06'. 90 + 160x + x2 = 0 Move the constant term to the right: Add '-90' to each side of the equation. 90 + 160x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + 160x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + 160x + x2 = 0 + -90 160x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 160x + x2 = -90 The x term is 160x. Take half its coefficient (80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. 160x + 6400 + x2 = -90 + 6400 Reorder the terms: 6400 + 160x + x2 = -90 + 6400 Combine like terms: -90 + 6400 = 6310 6400 + 160x + x2 = 6310 Factor a perfect square on the left side: (x + 80)(x + 80) = 6310 Calculate the square root of the right side: 79.435508433 Break this problem into two subproblems by setting (x + 80) equal to 79.435508433 and -79.435508433.Subproblem 1
x + 80 = 79.435508433 Simplifying x + 80 = 79.435508433 Reorder the terms: 80 + x = 79.435508433 Solving 80 + x = 79.435508433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = 79.435508433 + -80 Combine like terms: 80 + -80 = 0 0 + x = 79.435508433 + -80 x = 79.435508433 + -80 Combine like terms: 79.435508433 + -80 = -0.564491567 x = -0.564491567 Simplifying x = -0.564491567Subproblem 2
x + 80 = -79.435508433 Simplifying x + 80 = -79.435508433 Reorder the terms: 80 + x = -79.435508433 Solving 80 + x = -79.435508433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = -79.435508433 + -80 Combine like terms: 80 + -80 = 0 0 + x = -79.435508433 + -80 x = -79.435508433 + -80 Combine like terms: -79.435508433 + -80 = -159.435508433 x = -159.435508433 Simplifying x = -159.435508433Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.564491567, -159.435508433}
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