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Simplifying 8x2 + 10x + -105 = 0 Reorder the terms: -105 + 10x + 8x2 = 0 Solving -105 + 10x + 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'. -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 = 3.051360292 x = 3.051360292 Simplifying x = 3.051360292Subproblem 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 = -4.301360292 x = -4.301360292 Simplifying x = -4.301360292Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.051360292, -4.301360292}
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