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Simplifying 10x2 + 36x = 32 Reorder the terms: 36x + 10x2 = 32 Solving 36x + 10x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 36x + 10x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 36x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 18x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + 18x + 5x2)' equal to zero and attempt to solve: Simplifying -16 + 18x + 5x2 = 0 Solving -16 + 18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + 3.6x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 3.6x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 3.6x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 3.6x + x2 = 0 + 3.2 3.6x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 3.6x + x2 = 3.2 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 3.2 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 3.2 + 3.24 Combine like terms: 3.2 + 3.24 = 6.44 3.24 + 3.6x + x2 = 6.44 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 6.44 Calculate the square root of the right side: 2.537715508 Break this problem into two subproblems by setting (x + 1.8) equal to 2.537715508 and -2.537715508.Subproblem 1
x + 1.8 = 2.537715508 Simplifying x + 1.8 = 2.537715508 Reorder the terms: 1.8 + x = 2.537715508 Solving 1.8 + x = 2.537715508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 2.537715508 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 2.537715508 + -1.8 x = 2.537715508 + -1.8 Combine like terms: 2.537715508 + -1.8 = 0.737715508 x = 0.737715508 Simplifying x = 0.737715508Subproblem 2
x + 1.8 = -2.537715508 Simplifying x + 1.8 = -2.537715508 Reorder the terms: 1.8 + x = -2.537715508 Solving 1.8 + x = -2.537715508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -2.537715508 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -2.537715508 + -1.8 x = -2.537715508 + -1.8 Combine like terms: -2.537715508 + -1.8 = -4.337715508 x = -4.337715508 Simplifying x = -4.337715508Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.737715508, -4.337715508}Solution
x = {0.737715508, -4.337715508}
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