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Simplifying 2x2 + -8x + 16 = 144 Reorder the terms: 16 + -8x + 2x2 = 144 Solving 16 + -8x + 2x2 = 144 Solving for variable 'x'. Reorder the terms: 16 + -144 + -8x + 2x2 = 144 + -144 Combine like terms: 16 + -144 = -128 -128 + -8x + 2x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -128 + -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-64 + -4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-64 + -4x + x2)' equal to zero and attempt to solve: Simplifying -64 + -4x + x2 = 0 Solving -64 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -4x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -4x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -4x + x2 = 0 + 64 -4x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -4x + x2 = 64 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 = 64 + 4 Reorder the terms: 4 + -4x + x2 = 64 + 4 Combine like terms: 64 + 4 = 68 4 + -4x + x2 = 68 Factor a perfect square on the left side: (x + -2)(x + -2) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x + -2) equal to 8.246211251 and -8.246211251.Subproblem 1
x + -2 = 8.246211251 Simplifying x + -2 = 8.246211251 Reorder the terms: -2 + x = 8.246211251 Solving -2 + x = 8.246211251 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 = 8.246211251 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.246211251 + 2 x = 8.246211251 + 2 Combine like terms: 8.246211251 + 2 = 10.246211251 x = 10.246211251 Simplifying x = 10.246211251Subproblem 2
x + -2 = -8.246211251 Simplifying x + -2 = -8.246211251 Reorder the terms: -2 + x = -8.246211251 Solving -2 + x = -8.246211251 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 = -8.246211251 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.246211251 + 2 x = -8.246211251 + 2 Combine like terms: -8.246211251 + 2 = -6.246211251 x = -6.246211251 Simplifying x = -6.246211251Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.246211251, -6.246211251}Solution
x = {10.246211251, -6.246211251}
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