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Simplifying 92 + 12x + -8x2 = 0 Solving 92 + 12x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(23 + 3x + -2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(23 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying 23 + 3x + -2x2 = 0 Solving 23 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -11.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -1.5x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -1.5x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -1.5x + x2 = 0 + 11.5 -1.5x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -1.5x + x2 = 11.5 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 = 11.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 11.5 + 0.5625 Combine like terms: 11.5 + 0.5625 = 12.0625 0.5625 + -1.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + -0.75) equal to 3.473110997 and -3.473110997.Subproblem 1
x + -0.75 = 3.473110997 Simplifying x + -0.75 = 3.473110997 Reorder the terms: -0.75 + x = 3.473110997 Solving -0.75 + x = 3.473110997 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 = 3.473110997 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.473110997 + 0.75 x = 3.473110997 + 0.75 Combine like terms: 3.473110997 + 0.75 = 4.223110997 x = 4.223110997 Simplifying x = 4.223110997Subproblem 2
x + -0.75 = -3.473110997 Simplifying x + -0.75 = -3.473110997 Reorder the terms: -0.75 + x = -3.473110997 Solving -0.75 + x = -3.473110997 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 = -3.473110997 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.473110997 + 0.75 x = -3.473110997 + 0.75 Combine like terms: -3.473110997 + 0.75 = -2.723110997 x = -2.723110997 Simplifying x = -2.723110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.223110997, -2.723110997}Solution
x = {4.223110997, -2.723110997}
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