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Simplifying 8x2 + -16x + -45 = 0 Reorder the terms: -45 + -16x + 8x2 = 0 Solving -45 + -16x + 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 + -2x + x2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -2x + 5.625 + x2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -2x + x2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -2x + x2 = 0 + 5.625 -2x + x2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -2x + x2 = 5.625 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 5.625 + 1 Reorder the terms: 1 + -2x + x2 = 5.625 + 1 Combine like terms: 5.625 + 1 = 6.625 1 + -2x + x2 = 6.625 Factor a perfect square on the left side: (x + -1)(x + -1) = 6.625 Calculate the square root of the right side: 2.573907535 Break this problem into two subproblems by setting (x + -1) equal to 2.573907535 and -2.573907535.Subproblem 1
x + -1 = 2.573907535 Simplifying x + -1 = 2.573907535 Reorder the terms: -1 + x = 2.573907535 Solving -1 + x = 2.573907535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.573907535 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.573907535 + 1 x = 2.573907535 + 1 Combine like terms: 2.573907535 + 1 = 3.573907535 x = 3.573907535 Simplifying x = 3.573907535Subproblem 2
x + -1 = -2.573907535 Simplifying x + -1 = -2.573907535 Reorder the terms: -1 + x = -2.573907535 Solving -1 + x = -2.573907535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.573907535 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.573907535 + 1 x = -2.573907535 + 1 Combine like terms: -2.573907535 + 1 = -1.573907535 x = -1.573907535 Simplifying x = -1.573907535Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.573907535, -1.573907535}
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