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Simplifying 0 = -8x2 + -12x + -3 Reorder the terms: 0 = -3 + -12x + -8x2 Solving 0 = -3 + -12x + -8x2 Solving for variable 'x'. Combine like terms: 0 + 3 = 3 3 + 12x + 8x2 = -3 + -12x + -8x2 + 3 + 12x + 8x2 Reorder the terms: 3 + 12x + 8x2 = -3 + 3 + -12x + 12x + -8x2 + 8x2 Combine like terms: -3 + 3 = 0 3 + 12x + 8x2 = 0 + -12x + 12x + -8x2 + 8x2 3 + 12x + 8x2 = -12x + 12x + -8x2 + 8x2 Combine like terms: -12x + 12x = 0 3 + 12x + 8x2 = 0 + -8x2 + 8x2 3 + 12x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 3 + 12x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 1.5x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 1.5x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 1.5x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 1.5x + x2 = 0 + -0.375 1.5x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 1.5x + x2 = -0.375 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 = -0.375 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -0.375 + 0.5625 Combine like terms: -0.375 + 0.5625 = 0.1875 0.5625 + 1.5x + x2 = 0.1875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 0.1875 Calculate the square root of the right side: 0.433012702 Break this problem into two subproblems by setting (x + 0.75) equal to 0.433012702 and -0.433012702.Subproblem 1
x + 0.75 = 0.433012702 Simplifying x + 0.75 = 0.433012702 Reorder the terms: 0.75 + x = 0.433012702 Solving 0.75 + x = 0.433012702 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 = 0.433012702 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.433012702 + -0.75 x = 0.433012702 + -0.75 Combine like terms: 0.433012702 + -0.75 = -0.316987298 x = -0.316987298 Simplifying x = -0.316987298Subproblem 2
x + 0.75 = -0.433012702 Simplifying x + 0.75 = -0.433012702 Reorder the terms: 0.75 + x = -0.433012702 Solving 0.75 + x = -0.433012702 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 = -0.433012702 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.433012702 + -0.75 x = -0.433012702 + -0.75 Combine like terms: -0.433012702 + -0.75 = -1.183012702 x = -1.183012702 Simplifying x = -1.183012702Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.316987298, -1.183012702}
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