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Simplifying 4x2 + 4x2 + 25 + 2x2 + -5x = 180 Reorder the terms: 25 + -5x + 4x2 + 4x2 + 2x2 = 180 Combine like terms: 4x2 + 4x2 = 8x2 25 + -5x + 8x2 + 2x2 = 180 Combine like terms: 8x2 + 2x2 = 10x2 25 + -5x + 10x2 = 180 Solving 25 + -5x + 10x2 = 180 Solving for variable 'x'. Reorder the terms: 25 + -180 + -5x + 10x2 = 180 + -180 Combine like terms: 25 + -180 = -155 -155 + -5x + 10x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -155 + -5x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-31 + -1x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-31 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -31 + -1x + 2x2 = 0 Solving -31 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '15.5' to each side of the equation. -15.5 + -0.5x + 15.5 + x2 = 0 + 15.5 Reorder the terms: -15.5 + 15.5 + -0.5x + x2 = 0 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + -0.5x + x2 = 0 + 15.5 -0.5x + x2 = 0 + 15.5 Combine like terms: 0 + 15.5 = 15.5 -0.5x + x2 = 15.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 15.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 15.5 + 0.0625 Combine like terms: 15.5 + 0.0625 = 15.5625 0.0625 + -0.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + -0.25) equal to 3.94493346 and -3.94493346.Subproblem 1
x + -0.25 = 3.94493346 Simplifying x + -0.25 = 3.94493346 Reorder the terms: -0.25 + x = 3.94493346 Solving -0.25 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 3.94493346 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.94493346 + 0.25 x = 3.94493346 + 0.25 Combine like terms: 3.94493346 + 0.25 = 4.19493346 x = 4.19493346 Simplifying x = 4.19493346Subproblem 2
x + -0.25 = -3.94493346 Simplifying x + -0.25 = -3.94493346 Reorder the terms: -0.25 + x = -3.94493346 Solving -0.25 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -3.94493346 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.94493346 + 0.25 x = -3.94493346 + 0.25 Combine like terms: -3.94493346 + 0.25 = -3.69493346 x = -3.69493346 Simplifying x = -3.69493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.19493346, -3.69493346}Solution
x = {4.19493346, -3.69493346}
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