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Simplifying 5x2 + 160x + 415 = 0 Reorder the terms: 415 + 160x + 5x2 = 0 Solving 415 + 160x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(83 + 32x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(83 + 32x + x2)' equal to zero and attempt to solve: Simplifying 83 + 32x + x2 = 0 Solving 83 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-83' to each side of the equation. 83 + 32x + -83 + x2 = 0 + -83 Reorder the terms: 83 + -83 + 32x + x2 = 0 + -83 Combine like terms: 83 + -83 = 0 0 + 32x + x2 = 0 + -83 32x + x2 = 0 + -83 Combine like terms: 0 + -83 = -83 32x + x2 = -83 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -83 + 256 Reorder the terms: 256 + 32x + x2 = -83 + 256 Combine like terms: -83 + 256 = 173 256 + 32x + x2 = 173 Factor a perfect square on the left side: (x + 16)(x + 16) = 173 Calculate the square root of the right side: 13.152946438 Break this problem into two subproblems by setting (x + 16) equal to 13.152946438 and -13.152946438.Subproblem 1
x + 16 = 13.152946438 Simplifying x + 16 = 13.152946438 Reorder the terms: 16 + x = 13.152946438 Solving 16 + x = 13.152946438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 13.152946438 + -16 Combine like terms: 16 + -16 = 0 0 + x = 13.152946438 + -16 x = 13.152946438 + -16 Combine like terms: 13.152946438 + -16 = -2.847053562 x = -2.847053562 Simplifying x = -2.847053562Subproblem 2
x + 16 = -13.152946438 Simplifying x + 16 = -13.152946438 Reorder the terms: 16 + x = -13.152946438 Solving 16 + x = -13.152946438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -13.152946438 + -16 Combine like terms: 16 + -16 = 0 0 + x = -13.152946438 + -16 x = -13.152946438 + -16 Combine like terms: -13.152946438 + -16 = -29.152946438 x = -29.152946438 Simplifying x = -29.152946438Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.847053562, -29.152946438}Solution
x = {-2.847053562, -29.152946438}
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