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Simplifying 8x2 + -49x + -45 = 0 Reorder the terms: -45 + -49x + 8x2 = 0 Solving -45 + -49x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + -6.125x + x2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -6.125x + 5.625 + x2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -6.125x + x2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -6.125x + x2 = 0 + 5.625 -6.125x + x2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -6.125x + x2 = 5.625 The x term is -6.125x. Take half its coefficient (-3.0625). Square it (9.37890625) and add it to both sides. Add '9.37890625' to each side of the equation. -6.125x + 9.37890625 + x2 = 5.625 + 9.37890625 Reorder the terms: 9.37890625 + -6.125x + x2 = 5.625 + 9.37890625 Combine like terms: 5.625 + 9.37890625 = 15.00390625 9.37890625 + -6.125x + x2 = 15.00390625 Factor a perfect square on the left side: (x + -3.0625)(x + -3.0625) = 15.00390625 Calculate the square root of the right side: 3.873487608 Break this problem into two subproblems by setting (x + -3.0625) equal to 3.873487608 and -3.873487608.Subproblem 1
x + -3.0625 = 3.873487608 Simplifying x + -3.0625 = 3.873487608 Reorder the terms: -3.0625 + x = 3.873487608 Solving -3.0625 + x = 3.873487608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + x = 3.873487608 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + x = 3.873487608 + 3.0625 x = 3.873487608 + 3.0625 Combine like terms: 3.873487608 + 3.0625 = 6.935987608 x = 6.935987608 Simplifying x = 6.935987608Subproblem 2
x + -3.0625 = -3.873487608 Simplifying x + -3.0625 = -3.873487608 Reorder the terms: -3.0625 + x = -3.873487608 Solving -3.0625 + x = -3.873487608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + x = -3.873487608 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + x = -3.873487608 + 3.0625 x = -3.873487608 + 3.0625 Combine like terms: -3.873487608 + 3.0625 = -0.810987608 x = -0.810987608 Simplifying x = -0.810987608Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.935987608, -0.810987608}
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