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Simplifying 0.8x2 + 3x + -720 = 0 Reorder the terms: -720 + 3x + 0.8x2 = 0 Solving -720 + 3x + 0.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -900 + 3.75x + x2 = 0 Move the constant term to the right: Add '900' to each side of the equation. -900 + 3.75x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 3.75x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 3.75x + x2 = 0 + 900 3.75x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 3.75x + x2 = 900 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 900 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 900 + 3.515625 Combine like terms: 900 + 3.515625 = 903.515625 3.515625 + 3.75x + x2 = 903.515625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 903.515625 Calculate the square root of the right side: 30.058536641 Break this problem into two subproblems by setting (x + 1.875) equal to 30.058536641 and -30.058536641.Subproblem 1
x + 1.875 = 30.058536641 Simplifying x + 1.875 = 30.058536641 Reorder the terms: 1.875 + x = 30.058536641 Solving 1.875 + x = 30.058536641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 30.058536641 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 30.058536641 + -1.875 x = 30.058536641 + -1.875 Combine like terms: 30.058536641 + -1.875 = 28.183536641 x = 28.183536641 Simplifying x = 28.183536641Subproblem 2
x + 1.875 = -30.058536641 Simplifying x + 1.875 = -30.058536641 Reorder the terms: 1.875 + x = -30.058536641 Solving 1.875 + x = -30.058536641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -30.058536641 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -30.058536641 + -1.875 x = -30.058536641 + -1.875 Combine like terms: -30.058536641 + -1.875 = -31.933536641 x = -31.933536641 Simplifying x = -31.933536641Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.183536641, -31.933536641}
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