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Simplifying 8x2 + -10x = 45 Reorder the terms: -10x + 8x2 = 45 Solving -10x + 8x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -10x + 8x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -10x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + -1.25x + x2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -1.25x + 5.625 + x2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -1.25x + x2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -1.25x + x2 = 0 + 5.625 -1.25x + x2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -1.25x + x2 = 5.625 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 = 5.625 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 5.625 + 0.390625 Combine like terms: 5.625 + 0.390625 = 6.015625 0.390625 + -1.25x + x2 = 6.015625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + -0.625) equal to 2.452677109 and -2.452677109.Subproblem 1
x + -0.625 = 2.452677109 Simplifying x + -0.625 = 2.452677109 Reorder the terms: -0.625 + x = 2.452677109 Solving -0.625 + x = 2.452677109 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 = 2.452677109 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.452677109 + 0.625 x = 2.452677109 + 0.625 Combine like terms: 2.452677109 + 0.625 = 3.077677109 x = 3.077677109 Simplifying x = 3.077677109Subproblem 2
x + -0.625 = -2.452677109 Simplifying x + -0.625 = -2.452677109 Reorder the terms: -0.625 + x = -2.452677109 Solving -0.625 + x = -2.452677109 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 = -2.452677109 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.452677109 + 0.625 x = -2.452677109 + 0.625 Combine like terms: -2.452677109 + 0.625 = -1.827677109 x = -1.827677109 Simplifying x = -1.827677109Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.077677109, -1.827677109}
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