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Simplifying 0 = 2.5 + 5.8x + -0.9x2 Solving 0 = 2.5 + 5.8x + -0.9x2 Solving for variable 'x'. Combine like terms: 0 + -2.5 = -2.5 -2.5 + -5.8x + 0.9x2 = 2.5 + 5.8x + -0.9x2 + -2.5 + -5.8x + 0.9x2 Reorder the terms: -2.5 + -5.8x + 0.9x2 = 2.5 + -2.5 + 5.8x + -5.8x + -0.9x2 + 0.9x2 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + -5.8x + 0.9x2 = 0.0 + 5.8x + -5.8x + -0.9x2 + 0.9x2 -2.5 + -5.8x + 0.9x2 = 5.8x + -5.8x + -0.9x2 + 0.9x2 Combine like terms: 5.8x + -5.8x = 0.0 -2.5 + -5.8x + 0.9x2 = 0.0 + -0.9x2 + 0.9x2 -2.5 + -5.8x + 0.9x2 = -0.9x2 + 0.9x2 Combine like terms: -0.9x2 + 0.9x2 = 0.0 -2.5 + -5.8x + 0.9x2 = 0.0 Begin completing the square. Divide all terms by 0.9 the coefficient of the squared term: Divide each side by '0.9'. -2.777777778 + -6.444444444x + x2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + -6.444444444x + 2.777777778 + x2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + -6.444444444x + x2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + -6.444444444x + x2 = 0 + 2.777777778 -6.444444444x + x2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 -6.444444444x + x2 = 2.777777778 The x term is -6.444444444x. Take half its coefficient (-3.222222222). Square it (10.38271605) and add it to both sides. Add '10.38271605' to each side of the equation. -6.444444444x + 10.38271605 + x2 = 2.777777778 + 10.38271605 Reorder the terms: 10.38271605 + -6.444444444x + x2 = 2.777777778 + 10.38271605 Combine like terms: 2.777777778 + 10.38271605 = 13.160493828 10.38271605 + -6.444444444x + x2 = 13.160493828 Factor a perfect square on the left side: (x + -3.222222222)(x + -3.222222222) = 13.160493828 Calculate the square root of the right side: 3.627739493 Break this problem into two subproblems by setting (x + -3.222222222) equal to 3.627739493 and -3.627739493.Subproblem 1
x + -3.222222222 = 3.627739493 Simplifying x + -3.222222222 = 3.627739493 Reorder the terms: -3.222222222 + x = 3.627739493 Solving -3.222222222 + x = 3.627739493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.222222222' to each side of the equation. -3.222222222 + 3.222222222 + x = 3.627739493 + 3.222222222 Combine like terms: -3.222222222 + 3.222222222 = 0.000000000 0.000000000 + x = 3.627739493 + 3.222222222 x = 3.627739493 + 3.222222222 Combine like terms: 3.627739493 + 3.222222222 = 6.849961715 x = 6.849961715 Simplifying x = 6.849961715Subproblem 2
x + -3.222222222 = -3.627739493 Simplifying x + -3.222222222 = -3.627739493 Reorder the terms: -3.222222222 + x = -3.627739493 Solving -3.222222222 + x = -3.627739493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.222222222' to each side of the equation. -3.222222222 + 3.222222222 + x = -3.627739493 + 3.222222222 Combine like terms: -3.222222222 + 3.222222222 = 0.000000000 0.000000000 + x = -3.627739493 + 3.222222222 x = -3.627739493 + 3.222222222 Combine like terms: -3.627739493 + 3.222222222 = -0.405517271 x = -0.405517271 Simplifying x = -0.405517271Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.849961715, -0.405517271}
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