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Simplifying 100 = x2 + x2 + 2x + 4 Reorder the terms: 100 = 4 + 2x + x2 + x2 Combine like terms: x2 + x2 = 2x2 100 = 4 + 2x + 2x2 Solving 100 = 4 + 2x + 2x2 Solving for variable 'x'. Combine like terms: 100 + -4 = 96 96 + -2x + -2x2 = 4 + 2x + 2x2 + -4 + -2x + -2x2 Reorder the terms: 96 + -2x + -2x2 = 4 + -4 + 2x + -2x + 2x2 + -2x2 Combine like terms: 4 + -4 = 0 96 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2 96 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 96 + -2x + -2x2 = 0 + 2x2 + -2x2 96 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 96 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + -1x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(48 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 48 + -1x + -1x2 = 0 Solving 48 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + x + x2 = 0 + 48 x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 x + x2 = 48 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 48 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 48 + 0.25 Combine like terms: 48 + 0.25 = 48.25 1.25 + x2 = 48.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + 0.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + 0.5 = 6.946221995 Simplifying x + 0.5 = 6.946221995 Reorder the terms: 0.5 + x = 6.946221995 Solving 0.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.946221995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.946221995 + -0.5 x = 6.946221995 + -0.5 Combine like terms: 6.946221995 + -0.5 = 6.446221995 x = 6.446221995 Simplifying x = 6.446221995Subproblem 2
x + 0.5 = -6.946221995 Simplifying x + 0.5 = -6.946221995 Reorder the terms: 0.5 + x = -6.946221995 Solving 0.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.946221995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.946221995 + -0.5 x = -6.946221995 + -0.5 Combine like terms: -6.946221995 + -0.5 = -7.446221995 x = -7.446221995 Simplifying x = -7.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.446221995, -7.446221995}Solution
x = {6.446221995, -7.446221995}
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