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Simplifying 5 = 0.8x(x + -9) Reorder the terms: 5 = 0.8x(-9 + x) 5 = (-9 * 0.8x + x * 0.8x) 5 = (-7.2x + 0.8x2) Solving 5 = -7.2x + 0.8x2 Solving for variable 'x'. Reorder the terms: 5 + 7.2x + -0.8x2 = -7.2x + 7.2x + 0.8x2 + -0.8x2 Combine like terms: -7.2x + 7.2x = 0.0 5 + 7.2x + -0.8x2 = 0.0 + 0.8x2 + -0.8x2 5 + 7.2x + -0.8x2 = 0.8x2 + -0.8x2 Combine like terms: 0.8x2 + -0.8x2 = 0.0 5 + 7.2x + -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'. -6.25 + -9x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -9x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -9x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -9x + x2 = 0 + 6.25 -9x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -9x + x2 = 6.25 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 6.25 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 6.25 + 20.25 Combine like terms: 6.25 + 20.25 = 26.5 20.25 + -9x + x2 = 26.5 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 26.5 Calculate the square root of the right side: 5.14781507 Break this problem into two subproblems by setting (x + -4.5) equal to 5.14781507 and -5.14781507.Subproblem 1
x + -4.5 = 5.14781507 Simplifying x + -4.5 = 5.14781507 Reorder the terms: -4.5 + x = 5.14781507 Solving -4.5 + x = 5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.14781507 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.14781507 + 4.5 x = 5.14781507 + 4.5 Combine like terms: 5.14781507 + 4.5 = 9.64781507 x = 9.64781507 Simplifying x = 9.64781507Subproblem 2
x + -4.5 = -5.14781507 Simplifying x + -4.5 = -5.14781507 Reorder the terms: -4.5 + x = -5.14781507 Solving -4.5 + x = -5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.14781507 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.14781507 + 4.5 x = -5.14781507 + 4.5 Combine like terms: -5.14781507 + 4.5 = -0.64781507 x = -0.64781507 Simplifying x = -0.64781507Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.64781507, -0.64781507}
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