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Simplifying 0 = 8x2 + -10x + -105 Reorder the terms: 0 = -105 + -10x + 8x2 Solving 0 = -105 + -10x + 8x2 Solving for variable 'x'. Combine like terms: 0 + 105 = 105 105 + 10x + -8x2 = -105 + -10x + 8x2 + 105 + 10x + -8x2 Reorder the terms: 105 + 10x + -8x2 = -105 + 105 + -10x + 10x + 8x2 + -8x2 Combine like terms: -105 + 105 = 0 105 + 10x + -8x2 = 0 + -10x + 10x + 8x2 + -8x2 105 + 10x + -8x2 = -10x + 10x + 8x2 + -8x2 Combine like terms: -10x + 10x = 0 105 + 10x + -8x2 = 0 + 8x2 + -8x2 105 + 10x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 105 + 10x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -13.125 + -1.25x + x2 = 0 Move the constant term to the right: Add '13.125' to each side of the equation. -13.125 + -1.25x + 13.125 + x2 = 0 + 13.125 Reorder the terms: -13.125 + 13.125 + -1.25x + x2 = 0 + 13.125 Combine like terms: -13.125 + 13.125 = 0.000 0.000 + -1.25x + x2 = 0 + 13.125 -1.25x + x2 = 0 + 13.125 Combine like terms: 0 + 13.125 = 13.125 -1.25x + x2 = 13.125 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 13.125 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 13.125 + 0.390625 Combine like terms: 13.125 + 0.390625 = 13.515625 0.390625 + -1.25x + x2 = 13.515625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 13.515625 Calculate the square root of the right side: 3.676360292 Break this problem into two subproblems by setting (x + -0.625) equal to 3.676360292 and -3.676360292.Subproblem 1
x + -0.625 = 3.676360292 Simplifying x + -0.625 = 3.676360292 Reorder the terms: -0.625 + x = 3.676360292 Solving -0.625 + x = 3.676360292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 3.676360292 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 3.676360292 + 0.625 x = 3.676360292 + 0.625 Combine like terms: 3.676360292 + 0.625 = 4.301360292 x = 4.301360292 Simplifying x = 4.301360292Subproblem 2
x + -0.625 = -3.676360292 Simplifying x + -0.625 = -3.676360292 Reorder the terms: -0.625 + x = -3.676360292 Solving -0.625 + x = -3.676360292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -3.676360292 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -3.676360292 + 0.625 x = -3.676360292 + 0.625 Combine like terms: -3.676360292 + 0.625 = -3.051360292 x = -3.051360292 Simplifying x = -3.051360292Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.301360292, -3.051360292}
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