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Simplifying 5x2 + 4x + 25 = 180 Reorder the terms: 25 + 4x + 5x2 = 180 Solving 25 + 4x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: 25 + -180 + 4x + 5x2 = 180 + -180 Combine like terms: 25 + -180 = -155 -155 + 4x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -155 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -31 + 0.8x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 0.8x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 0.8x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 0.8x + x2 = 0 + 31 0.8x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 0.8x + x2 = 31 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 31 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 31 + 0.16 Combine like terms: 31 + 0.16 = 31.16 0.16 + 0.8x + x2 = 31.16 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 31.16 Calculate the square root of the right side: 5.582114295 Break this problem into two subproblems by setting (x + 0.4) equal to 5.582114295 and -5.582114295.Subproblem 1
x + 0.4 = 5.582114295 Simplifying x + 0.4 = 5.582114295 Reorder the terms: 0.4 + x = 5.582114295 Solving 0.4 + x = 5.582114295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 5.582114295 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 5.582114295 + -0.4 x = 5.582114295 + -0.4 Combine like terms: 5.582114295 + -0.4 = 5.182114295 x = 5.182114295 Simplifying x = 5.182114295Subproblem 2
x + 0.4 = -5.582114295 Simplifying x + 0.4 = -5.582114295 Reorder the terms: 0.4 + x = -5.582114295 Solving 0.4 + x = -5.582114295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -5.582114295 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -5.582114295 + -0.4 x = -5.582114295 + -0.4 Combine like terms: -5.582114295 + -0.4 = -5.982114295 x = -5.982114295 Simplifying x = -5.982114295Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.182114295, -5.982114295}
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