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Simplifying 0 = 2x2 + 8x + -1056 Reorder the terms: 0 = -1056 + 8x + 2x2 Solving 0 = -1056 + 8x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 1056 = 1056 1056 + -8x + -2x2 = -1056 + 8x + 2x2 + 1056 + -8x + -2x2 Reorder the terms: 1056 + -8x + -2x2 = -1056 + 1056 + 8x + -8x + 2x2 + -2x2 Combine like terms: -1056 + 1056 = 0 1056 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2 1056 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 1056 + -8x + -2x2 = 0 + 2x2 + -2x2 1056 + -8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1056 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(528 + -4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(528 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 528 + -4x + -1x2 = 0 Solving 528 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -528 + 4x + x2 = 0 Move the constant term to the right: Add '528' to each side of the equation. -528 + 4x + 528 + x2 = 0 + 528 Reorder the terms: -528 + 528 + 4x + x2 = 0 + 528 Combine like terms: -528 + 528 = 0 0 + 4x + x2 = 0 + 528 4x + x2 = 0 + 528 Combine like terms: 0 + 528 = 528 4x + x2 = 528 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 528 + 4 Reorder the terms: 4 + 4x + x2 = 528 + 4 Combine like terms: 528 + 4 = 532 4 + 4x + x2 = 532 Factor a perfect square on the left side: (x + 2)(x + 2) = 532 Calculate the square root of the right side: 23.065125189 Break this problem into two subproblems by setting (x + 2) equal to 23.065125189 and -23.065125189.Subproblem 1
x + 2 = 23.065125189 Simplifying x + 2 = 23.065125189 Reorder the terms: 2 + x = 23.065125189 Solving 2 + x = 23.065125189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 23.065125189 + -2 Combine like terms: 2 + -2 = 0 0 + x = 23.065125189 + -2 x = 23.065125189 + -2 Combine like terms: 23.065125189 + -2 = 21.065125189 x = 21.065125189 Simplifying x = 21.065125189Subproblem 2
x + 2 = -23.065125189 Simplifying x + 2 = -23.065125189 Reorder the terms: 2 + x = -23.065125189 Solving 2 + x = -23.065125189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -23.065125189 + -2 Combine like terms: 2 + -2 = 0 0 + x = -23.065125189 + -2 x = -23.065125189 + -2 Combine like terms: -23.065125189 + -2 = -25.065125189 x = -25.065125189 Simplifying x = -25.065125189Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.065125189, -25.065125189}Solution
x = {21.065125189, -25.065125189}
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