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Simplifying -6x2 + 3x + 69 = 0 Reorder the terms: 69 + 3x + -6x2 = 0 Solving 69 + 3x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(23 + x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(23 + x + -2x2)' equal to zero and attempt to solve: Simplifying 23 + x + -2x2 = 0 Solving 23 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -11.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -0.5x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -0.5x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -0.5x + x2 = 0 + 11.5 -0.5x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -0.5x + x2 = 11.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5x + 0.25 + x2 = 11.5 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = 11.5 + 0.25 Combine like terms: 11.5 + 0.25 = 11.75 0.25 + -0.5x + x2 = 11.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (x + 0.5) equal to 3.4278273 and -3.4278273.Subproblem 1
x + 0.5 = 3.4278273 Simplifying x + 0.5 = 3.4278273 Reorder the terms: 0.5 + x = 3.4278273 Solving 0.5 + x = 3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.4278273 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.4278273 + -0.5 x = 3.4278273 + -0.5 Combine like terms: 3.4278273 + -0.5 = 2.9278273 x = 2.9278273 Simplifying x = 2.9278273Subproblem 2
x + 0.5 = -3.4278273 Simplifying x + 0.5 = -3.4278273 Reorder the terms: 0.5 + x = -3.4278273 Solving 0.5 + x = -3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.4278273 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.4278273 + -0.5 x = -3.4278273 + -0.5 Combine like terms: -3.4278273 + -0.5 = -3.9278273 x = -3.9278273 Simplifying x = -3.9278273Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9278273, -3.9278273}Solution
x = {2.9278273, -3.9278273}
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