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Simplifying 720 = 2x2 + 6x Reorder the terms: 720 = 6x + 2x2 Solving 720 = 6x + 2x2 Solving for variable 'x'. Reorder the terms: 720 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 720 + -6x + -2x2 = 0 + 2x2 + -2x2 720 + -6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 720 + -6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(360 + -3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(360 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 360 + -3x + -1x2 = 0 Solving 360 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -360 + 3x + x2 = 0 Move the constant term to the right: Add '360' to each side of the equation. -360 + 3x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 3x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 3x + x2 = 0 + 360 3x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 3x + x2 = 360 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 360 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 360 + 2.25 Combine like terms: 360 + 2.25 = 362.25 2.25 + 3x + x2 = 362.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 362.25 Calculate the square root of the right side: 19.032866311 Break this problem into two subproblems by setting (x + 1.5) equal to 19.032866311 and -19.032866311.Subproblem 1
x + 1.5 = 19.032866311 Simplifying x + 1.5 = 19.032866311 Reorder the terms: 1.5 + x = 19.032866311 Solving 1.5 + x = 19.032866311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 19.032866311 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 19.032866311 + -1.5 x = 19.032866311 + -1.5 Combine like terms: 19.032866311 + -1.5 = 17.532866311 x = 17.532866311 Simplifying x = 17.532866311Subproblem 2
x + 1.5 = -19.032866311 Simplifying x + 1.5 = -19.032866311 Reorder the terms: 1.5 + x = -19.032866311 Solving 1.5 + x = -19.032866311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -19.032866311 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -19.032866311 + -1.5 x = -19.032866311 + -1.5 Combine like terms: -19.032866311 + -1.5 = -20.532866311 x = -20.532866311 Simplifying x = -20.532866311Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.532866311, -20.532866311}Solution
x = {17.532866311, -20.532866311}
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