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Simplifying 4x2 + 52x = 100 Reorder the terms: 52x + 4x2 = 100 Solving 52x + 4x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 52x + 4x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 52x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + 13x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + 13x + x2)' equal to zero and attempt to solve: Simplifying -25 + 13x + x2 = 0 Solving -25 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 13x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 13x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 13x + x2 = 0 + 25 13x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 13x + x2 = 25 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 25 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 25 + 42.25 Combine like terms: 25 + 42.25 = 67.25 42.25 + 13x + x2 = 67.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 67.25 Calculate the square root of the right side: 8.200609733 Break this problem into two subproblems by setting (x + 6.5) equal to 8.200609733 and -8.200609733.Subproblem 1
x + 6.5 = 8.200609733 Simplifying x + 6.5 = 8.200609733 Reorder the terms: 6.5 + x = 8.200609733 Solving 6.5 + x = 8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 8.200609733 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 8.200609733 + -6.5 x = 8.200609733 + -6.5 Combine like terms: 8.200609733 + -6.5 = 1.700609733 x = 1.700609733 Simplifying x = 1.700609733Subproblem 2
x + 6.5 = -8.200609733 Simplifying x + 6.5 = -8.200609733 Reorder the terms: 6.5 + x = -8.200609733 Solving 6.5 + x = -8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -8.200609733 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -8.200609733 + -6.5 x = -8.200609733 + -6.5 Combine like terms: -8.200609733 + -6.5 = -14.700609733 x = -14.700609733 Simplifying x = -14.700609733Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.700609733, -14.700609733}Solution
x = {1.700609733, -14.700609733}
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