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Simplifying 4x2 + -40x + 45 = 0 Reorder the terms: 45 + -40x + 4x2 = 0 Solving 45 + -40x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11.25 + -10x + x2 = 0 Move the constant term to the right: Add '-11.25' to each side of the equation. 11.25 + -10x + -11.25 + x2 = 0 + -11.25 Reorder the terms: 11.25 + -11.25 + -10x + x2 = 0 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + -10x + x2 = 0 + -11.25 -10x + x2 = 0 + -11.25 Combine like terms: 0 + -11.25 = -11.25 -10x + x2 = -11.25 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -11.25 + 25 Reorder the terms: 25 + -10x + x2 = -11.25 + 25 Combine like terms: -11.25 + 25 = 13.75 25 + -10x + x2 = 13.75 Factor a perfect square on the left side: (x + -5)(x + -5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (x + -5) equal to 3.708099244 and -3.708099244.Subproblem 1
x + -5 = 3.708099244 Simplifying x + -5 = 3.708099244 Reorder the terms: -5 + x = 3.708099244 Solving -5 + x = 3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.708099244 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.708099244 + 5 x = 3.708099244 + 5 Combine like terms: 3.708099244 + 5 = 8.708099244 x = 8.708099244 Simplifying x = 8.708099244Subproblem 2
x + -5 = -3.708099244 Simplifying x + -5 = -3.708099244 Reorder the terms: -5 + x = -3.708099244 Solving -5 + x = -3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.708099244 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.708099244 + 5 x = -3.708099244 + 5 Combine like terms: -3.708099244 + 5 = 1.291900756 x = 1.291900756 Simplifying x = 1.291900756Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.708099244, 1.291900756}
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