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Simplifying 4x2 + -6x = 16384 Reorder the terms: -6x + 4x2 = 16384 Solving -6x + 4x2 = 16384 Solving for variable 'x'. Reorder the terms: -16384 + -6x + 4x2 = 16384 + -16384 Combine like terms: 16384 + -16384 = 0 -16384 + -6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8192 + -3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8192 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying -8192 + -3x + 2x2 = 0 Solving -8192 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4096 + -1.5x + x2 = 0 Move the constant term to the right: Add '4096' to each side of the equation. -4096 + -1.5x + 4096 + x2 = 0 + 4096 Reorder the terms: -4096 + 4096 + -1.5x + x2 = 0 + 4096 Combine like terms: -4096 + 4096 = 0 0 + -1.5x + x2 = 0 + 4096 -1.5x + x2 = 0 + 4096 Combine like terms: 0 + 4096 = 4096 -1.5x + x2 = 4096 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 4096 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 4096 + 0.5625 Combine like terms: 4096 + 0.5625 = 4096.5625 0.5625 + -1.5x + x2 = 4096.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 4096.5625 Calculate the square root of the right side: 64.00439438 Break this problem into two subproblems by setting (x + -0.75) equal to 64.00439438 and -64.00439438.Subproblem 1
x + -0.75 = 64.00439438 Simplifying x + -0.75 = 64.00439438 Reorder the terms: -0.75 + x = 64.00439438 Solving -0.75 + x = 64.00439438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 64.00439438 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 64.00439438 + 0.75 x = 64.00439438 + 0.75 Combine like terms: 64.00439438 + 0.75 = 64.75439438 x = 64.75439438 Simplifying x = 64.75439438Subproblem 2
x + -0.75 = -64.00439438 Simplifying x + -0.75 = -64.00439438 Reorder the terms: -0.75 + x = -64.00439438 Solving -0.75 + x = -64.00439438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -64.00439438 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -64.00439438 + 0.75 x = -64.00439438 + 0.75 Combine like terms: -64.00439438 + 0.75 = -63.25439438 x = -63.25439438 Simplifying x = -63.25439438Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.75439438, -63.25439438}Solution
x = {64.75439438, -63.25439438}
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