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Simplifying 2x2 + 8x = 180 Reorder the terms: 8x + 2x2 = 180 Solving 8x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 8x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 4x + x2)' equal to zero and attempt to solve: Simplifying -90 + 4x + x2 = 0 Solving -90 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 4x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 4x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 4x + x2 = 0 + 90 4x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 4x + x2 = 90 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 90 + 4 Reorder the terms: 4 + 4x + x2 = 90 + 4 Combine like terms: 90 + 4 = 94 4 + 4x + x2 = 94 Factor a perfect square on the left side: (x + 2)(x + 2) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + 2) equal to 9.695359715 and -9.695359715.Subproblem 1
x + 2 = 9.695359715 Simplifying x + 2 = 9.695359715 Reorder the terms: 2 + x = 9.695359715 Solving 2 + x = 9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.695359715 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.695359715 + -2 x = 9.695359715 + -2 Combine like terms: 9.695359715 + -2 = 7.695359715 x = 7.695359715 Simplifying x = 7.695359715Subproblem 2
x + 2 = -9.695359715 Simplifying x + 2 = -9.695359715 Reorder the terms: 2 + x = -9.695359715 Solving 2 + x = -9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.695359715 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.695359715 + -2 x = -9.695359715 + -2 Combine like terms: -9.695359715 + -2 = -11.695359715 x = -11.695359715 Simplifying x = -11.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.695359715, -11.695359715}Solution
x = {7.695359715, -11.695359715}
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