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Simplifying 32x + 2x2 = 30 Solving 32x + 2x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 32x + 2x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 32x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 16x + x2)' equal to zero and attempt to solve: Simplifying -15 + 16x + x2 = 0 Solving -15 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 16x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 16x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 16x + x2 = 0 + 15 16x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 16x + x2 = 15 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 15 + 64 Reorder the terms: 64 + 16x + x2 = 15 + 64 Combine like terms: 15 + 64 = 79 64 + 16x + x2 = 79 Factor a perfect square on the left side: (x + 8)(x + 8) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + 8) equal to 8.888194417 and -8.888194417.Subproblem 1
x + 8 = 8.888194417 Simplifying x + 8 = 8.888194417 Reorder the terms: 8 + x = 8.888194417 Solving 8 + x = 8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 8.888194417 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.888194417 + -8 x = 8.888194417 + -8 Combine like terms: 8.888194417 + -8 = 0.888194417 x = 0.888194417 Simplifying x = 0.888194417Subproblem 2
x + 8 = -8.888194417 Simplifying x + 8 = -8.888194417 Reorder the terms: 8 + x = -8.888194417 Solving 8 + x = -8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -8.888194417 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.888194417 + -8 x = -8.888194417 + -8 Combine like terms: -8.888194417 + -8 = -16.888194417 x = -16.888194417 Simplifying x = -16.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.888194417, -16.888194417}Solution
x = {0.888194417, -16.888194417}
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