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Simplifying 936 = 2x2 + 2x + -24 Reorder the terms: 936 = -24 + 2x + 2x2 Solving 936 = -24 + 2x + 2x2 Solving for variable 'x'. Combine like terms: 936 + 24 = 960 960 + -2x + -2x2 = -24 + 2x + 2x2 + 24 + -2x + -2x2 Reorder the terms: 960 + -2x + -2x2 = -24 + 24 + 2x + -2x + 2x2 + -2x2 Combine like terms: -24 + 24 = 0 960 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2 960 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 960 + -2x + -2x2 = 0 + 2x2 + -2x2 960 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 960 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(480 + -1x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(480 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 480 + -1x + -1x2 = 0 Solving 480 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -480 + x + x2 = 0 Move the constant term to the right: Add '480' to each side of the equation. -480 + x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + x + x2 = 0 + 480 x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 x + x2 = 480 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 480 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 480 + 0.25 Combine like terms: 480 + 0.25 = 480.25 1.25 + x2 = 480.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 480.25 Calculate the square root of the right side: 21.914607001 Break this problem into two subproblems by setting (x + 0.5) equal to 21.914607001 and -21.914607001.Subproblem 1
x + 0.5 = 21.914607001 Simplifying x + 0.5 = 21.914607001 Reorder the terms: 0.5 + x = 21.914607001 Solving 0.5 + x = 21.914607001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 21.914607001 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 21.914607001 + -0.5 x = 21.914607001 + -0.5 Combine like terms: 21.914607001 + -0.5 = 21.414607001 x = 21.414607001 Simplifying x = 21.414607001Subproblem 2
x + 0.5 = -21.914607001 Simplifying x + 0.5 = -21.914607001 Reorder the terms: 0.5 + x = -21.914607001 Solving 0.5 + x = -21.914607001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -21.914607001 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -21.914607001 + -0.5 x = -21.914607001 + -0.5 Combine like terms: -21.914607001 + -0.5 = -22.414607001 x = -22.414607001 Simplifying x = -22.414607001Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.414607001, -22.414607001}Solution
x = {21.414607001, -22.414607001}
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