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Simplifying 720 = 0.8x2 + 4x Reorder the terms: 720 = 4x + 0.8x2 Solving 720 = 4x + 0.8x2 Solving for variable 'x'. Reorder the terms: 720 + -4x + -0.8x2 = 4x + -4x + 0.8x2 + -0.8x2 Combine like terms: 4x + -4x = 0 720 + -4x + -0.8x2 = 0 + 0.8x2 + -0.8x2 720 + -4x + -0.8x2 = 0.8x2 + -0.8x2 Combine like terms: 0.8x2 + -0.8x2 = 0.0 720 + -4x + -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'. -900 + 5x + x2 = 0 Move the constant term to the right: Add '900' to each side of the equation. -900 + 5x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 5x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 5x + x2 = 0 + 900 5x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 5x + x2 = 900 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 900 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 900 + 6.25 Combine like terms: 900 + 6.25 = 906.25 6.25 + 5x + x2 = 906.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 906.25 Calculate the square root of the right side: 30.103986447 Break this problem into two subproblems by setting (x + 2.5) equal to 30.103986447 and -30.103986447.Subproblem 1
x + 2.5 = 30.103986447 Simplifying x + 2.5 = 30.103986447 Reorder the terms: 2.5 + x = 30.103986447 Solving 2.5 + x = 30.103986447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 30.103986447 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 30.103986447 + -2.5 x = 30.103986447 + -2.5 Combine like terms: 30.103986447 + -2.5 = 27.603986447 x = 27.603986447 Simplifying x = 27.603986447Subproblem 2
x + 2.5 = -30.103986447 Simplifying x + 2.5 = -30.103986447 Reorder the terms: 2.5 + x = -30.103986447 Solving 2.5 + x = -30.103986447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -30.103986447 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -30.103986447 + -2.5 x = -30.103986447 + -2.5 Combine like terms: -30.103986447 + -2.5 = -32.603986447 x = -32.603986447 Simplifying x = -32.603986447Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.603986447, -32.603986447}
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