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Simplifying 936 = 2x2 + -4x + -32 Reorder the terms: 936 = -32 + -4x + 2x2 Solving 936 = -32 + -4x + 2x2 Solving for variable 'x'. Combine like terms: 936 + 32 = 968 968 + 4x + -2x2 = -32 + -4x + 2x2 + 32 + 4x + -2x2 Reorder the terms: 968 + 4x + -2x2 = -32 + 32 + -4x + 4x + 2x2 + -2x2 Combine like terms: -32 + 32 = 0 968 + 4x + -2x2 = 0 + -4x + 4x + 2x2 + -2x2 968 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 968 + 4x + -2x2 = 0 + 2x2 + -2x2 968 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 968 + 4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(484 + 2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(484 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 484 + 2x + -1x2 = 0 Solving 484 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -484 + -2x + x2 = 0 Move the constant term to the right: Add '484' to each side of the equation. -484 + -2x + 484 + x2 = 0 + 484 Reorder the terms: -484 + 484 + -2x + x2 = 0 + 484 Combine like terms: -484 + 484 = 0 0 + -2x + x2 = 0 + 484 -2x + x2 = 0 + 484 Combine like terms: 0 + 484 = 484 -2x + x2 = 484 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 484 + 1 Reorder the terms: 1 + -2x + x2 = 484 + 1 Combine like terms: 484 + 1 = 485 1 + -2x + x2 = 485 Factor a perfect square on the left side: (x + -1)(x + -1) = 485 Calculate the square root of the right side: 22.022715546 Break this problem into two subproblems by setting (x + -1) equal to 22.022715546 and -22.022715546.Subproblem 1
x + -1 = 22.022715546 Simplifying x + -1 = 22.022715546 Reorder the terms: -1 + x = 22.022715546 Solving -1 + x = 22.022715546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 22.022715546 + 1 Combine like terms: -1 + 1 = 0 0 + x = 22.022715546 + 1 x = 22.022715546 + 1 Combine like terms: 22.022715546 + 1 = 23.022715546 x = 23.022715546 Simplifying x = 23.022715546Subproblem 2
x + -1 = -22.022715546 Simplifying x + -1 = -22.022715546 Reorder the terms: -1 + x = -22.022715546 Solving -1 + x = -22.022715546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -22.022715546 + 1 Combine like terms: -1 + 1 = 0 0 + x = -22.022715546 + 1 x = -22.022715546 + 1 Combine like terms: -22.022715546 + 1 = -21.022715546 x = -21.022715546 Simplifying x = -21.022715546Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.022715546, -21.022715546}Solution
x = {23.022715546, -21.022715546}
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