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Simplifying 2x2 + 8x + 4 = 100 Reorder the terms: 4 + 8x + 2x2 = 100 Solving 4 + 8x + 2x2 = 100 Solving for variable 'x'. Reorder the terms: 4 + -100 + 8x + 2x2 = 100 + -100 Combine like terms: 4 + -100 = -96 -96 + 8x + 2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -96 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-48 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-48 + 4x + x2)' equal to zero and attempt to solve: Simplifying -48 + 4x + x2 = 0 Solving -48 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 4x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 4x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 4x + x2 = 0 + 48 4x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 4x + x2 = 48 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 48 + 4 Reorder the terms: 4 + 4x + x2 = 48 + 4 Combine like terms: 48 + 4 = 52 4 + 4x + x2 = 52 Factor a perfect square on the left side: (x + 2)(x + 2) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + 2) equal to 7.211102551 and -7.211102551.Subproblem 1
x + 2 = 7.211102551 Simplifying x + 2 = 7.211102551 Reorder the terms: 2 + x = 7.211102551 Solving 2 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 7.211102551 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.211102551 + -2 x = 7.211102551 + -2 Combine like terms: 7.211102551 + -2 = 5.211102551 x = 5.211102551 Simplifying x = 5.211102551Subproblem 2
x + 2 = -7.211102551 Simplifying x + 2 = -7.211102551 Reorder the terms: 2 + x = -7.211102551 Solving 2 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -7.211102551 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.211102551 + -2 x = -7.211102551 + -2 Combine like terms: -7.211102551 + -2 = -9.211102551 x = -9.211102551 Simplifying x = -9.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.211102551, -9.211102551}Solution
x = {5.211102551, -9.211102551}
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