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Simplifying 0 = 2x2 + 8x + -756 Reorder the terms: 0 = -756 + 8x + 2x2 Solving 0 = -756 + 8x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 756 = 756 756 + -8x + -2x2 = -756 + 8x + 2x2 + 756 + -8x + -2x2 Reorder the terms: 756 + -8x + -2x2 = -756 + 756 + 8x + -8x + 2x2 + -2x2 Combine like terms: -756 + 756 = 0 756 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2 756 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 756 + -8x + -2x2 = 0 + 2x2 + -2x2 756 + -8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 756 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(378 + -4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(378 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 378 + -4x + -1x2 = 0 Solving 378 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -378 + 4x + x2 = 0 Move the constant term to the right: Add '378' to each side of the equation. -378 + 4x + 378 + x2 = 0 + 378 Reorder the terms: -378 + 378 + 4x + x2 = 0 + 378 Combine like terms: -378 + 378 = 0 0 + 4x + x2 = 0 + 378 4x + x2 = 0 + 378 Combine like terms: 0 + 378 = 378 4x + x2 = 378 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 = 378 + 4 Reorder the terms: 4 + 4x + x2 = 378 + 4 Combine like terms: 378 + 4 = 382 4 + 4x + x2 = 382 Factor a perfect square on the left side: (x + 2)(x + 2) = 382 Calculate the square root of the right side: 19.544820286 Break this problem into two subproblems by setting (x + 2) equal to 19.544820286 and -19.544820286.Subproblem 1
x + 2 = 19.544820286 Simplifying x + 2 = 19.544820286 Reorder the terms: 2 + x = 19.544820286 Solving 2 + x = 19.544820286 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 = 19.544820286 + -2 Combine like terms: 2 + -2 = 0 0 + x = 19.544820286 + -2 x = 19.544820286 + -2 Combine like terms: 19.544820286 + -2 = 17.544820286 x = 17.544820286 Simplifying x = 17.544820286Subproblem 2
x + 2 = -19.544820286 Simplifying x + 2 = -19.544820286 Reorder the terms: 2 + x = -19.544820286 Solving 2 + x = -19.544820286 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 = -19.544820286 + -2 Combine like terms: 2 + -2 = 0 0 + x = -19.544820286 + -2 x = -19.544820286 + -2 Combine like terms: -19.544820286 + -2 = -21.544820286 x = -21.544820286 Simplifying x = -21.544820286Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.544820286, -21.544820286}Solution
x = {17.544820286, -21.544820286}
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