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Simplifying -0.8x(x + -9) = 1.7x + 5.6 Reorder the terms: -0.8x(-9 + x) = 1.7x + 5.6 (-9 * -0.8x + x * -0.8x) = 1.7x + 5.6 (7.2x + -0.8x2) = 1.7x + 5.6 Reorder the terms: 7.2x + -0.8x2 = 5.6 + 1.7x Solving 7.2x + -0.8x2 = 5.6 + 1.7x Solving for variable 'x'. Reorder the terms: -5.6 + 7.2x + -1.7x + -0.8x2 = 5.6 + 1.7x + -5.6 + -1.7x Combine like terms: 7.2x + -1.7x = 5.5x -5.6 + 5.5x + -0.8x2 = 5.6 + 1.7x + -5.6 + -1.7x Reorder the terms: -5.6 + 5.5x + -0.8x2 = 5.6 + -5.6 + 1.7x + -1.7x Combine like terms: 5.6 + -5.6 = 0.0 -5.6 + 5.5x + -0.8x2 = 0.0 + 1.7x + -1.7x -5.6 + 5.5x + -0.8x2 = 1.7x + -1.7x Combine like terms: 1.7x + -1.7x = 0.0 -5.6 + 5.5x + -0.8x2 = 0.0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 7 + -6.875x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6.875x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -6.875x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6.875x + x2 = 0 + -7 -6.875x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6.875x + x2 = -7 The x term is -6.875x. Take half its coefficient (-3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. -6.875x + 11.81640625 + x2 = -7 + 11.81640625 Reorder the terms: 11.81640625 + -6.875x + x2 = -7 + 11.81640625 Combine like terms: -7 + 11.81640625 = 4.81640625 11.81640625 + -6.875x + x2 = 4.81640625 Factor a perfect square on the left side: (x + -3.4375)(x + -3.4375) = 4.81640625 Calculate the square root of the right side: 2.194631233 Break this problem into two subproblems by setting (x + -3.4375) equal to 2.194631233 and -2.194631233.Subproblem 1
x + -3.4375 = 2.194631233 Simplifying x + -3.4375 = 2.194631233 Reorder the terms: -3.4375 + x = 2.194631233 Solving -3.4375 + x = 2.194631233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + x = 2.194631233 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = 2.194631233 + 3.4375 x = 2.194631233 + 3.4375 Combine like terms: 2.194631233 + 3.4375 = 5.632131233 x = 5.632131233 Simplifying x = 5.632131233Subproblem 2
x + -3.4375 = -2.194631233 Simplifying x + -3.4375 = -2.194631233 Reorder the terms: -3.4375 + x = -2.194631233 Solving -3.4375 + x = -2.194631233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + x = -2.194631233 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = -2.194631233 + 3.4375 x = -2.194631233 + 3.4375 Combine like terms: -2.194631233 + 3.4375 = 1.242868767 x = 1.242868767 Simplifying x = 1.242868767Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.632131233, 1.242868767}
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