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Simplifying 5x2 + -8x + -45 = 0 Reorder the terms: -45 + -8x + 5x2 = 0 Solving -45 + -8x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9 + -1.6x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -1.6x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -1.6x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1.6x + x2 = 0 + 9 -1.6x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1.6x + x2 = 9 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 9 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 9 + 0.64 Combine like terms: 9 + 0.64 = 9.64 0.64 + -1.6x + x2 = 9.64 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 9.64 Calculate the square root of the right side: 3.104834939 Break this problem into two subproblems by setting (x + -0.8) equal to 3.104834939 and -3.104834939.Subproblem 1
x + -0.8 = 3.104834939 Simplifying x + -0.8 = 3.104834939 Reorder the terms: -0.8 + x = 3.104834939 Solving -0.8 + x = 3.104834939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 3.104834939 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 3.104834939 + 0.8 x = 3.104834939 + 0.8 Combine like terms: 3.104834939 + 0.8 = 3.904834939 x = 3.904834939 Simplifying x = 3.904834939Subproblem 2
x + -0.8 = -3.104834939 Simplifying x + -0.8 = -3.104834939 Reorder the terms: -0.8 + x = -3.104834939 Solving -0.8 + x = -3.104834939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -3.104834939 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -3.104834939 + 0.8 x = -3.104834939 + 0.8 Combine like terms: -3.104834939 + 0.8 = -2.304834939 x = -2.304834939 Simplifying x = -2.304834939Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.904834939, -2.304834939}
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