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Simplifying 2x2 + 10x = 32 Reorder the terms: 10x + 2x2 = 32 Solving 10x + 2x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 10x + 2x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + 5x + x2)' equal to zero and attempt to solve: Simplifying -16 + 5x + x2 = 0 Solving -16 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 5x + x2 = 0 + 16 5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 5x + x2 = 16 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 16 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 16 + 6.25 Combine like terms: 16 + 6.25 = 22.25 6.25 + 5x + x2 = 22.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + 2.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + 2.5 = 4.716990566 Simplifying x + 2.5 = 4.716990566 Reorder the terms: 2.5 + x = 4.716990566 Solving 2.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.716990566 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.716990566 + -2.5 x = 4.716990566 + -2.5 Combine like terms: 4.716990566 + -2.5 = 2.216990566 x = 2.216990566 Simplifying x = 2.216990566Subproblem 2
x + 2.5 = -4.716990566 Simplifying x + 2.5 = -4.716990566 Reorder the terms: 2.5 + x = -4.716990566 Solving 2.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.716990566 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.716990566 + -2.5 x = -4.716990566 + -2.5 Combine like terms: -4.716990566 + -2.5 = -7.216990566 x = -7.216990566 Simplifying x = -7.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.216990566, -7.216990566}Solution
x = {2.216990566, -7.216990566}
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