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Simplifying 4x2 + 28x = -4 Reorder the terms: 28x + 4x2 = -4 Solving 28x + 4x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + 28x + 4x2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 28x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 7x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 7x + x2)' equal to zero and attempt to solve: Simplifying 1 + 7x + x2 = 0 Solving 1 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 7x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 7x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7x + x2 = 0 + -1 7x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 7x + x2 = -1 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -1 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -1 + 12.25 Combine like terms: -1 + 12.25 = 11.25 12.25 + 7x + x2 = 11.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + 3.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + 3.5 = 3.354101966 Simplifying x + 3.5 = 3.354101966 Reorder the terms: 3.5 + x = 3.354101966 Solving 3.5 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.354101966 + -3.5 x = 3.354101966 + -3.5 Combine like terms: 3.354101966 + -3.5 = -0.145898034 x = -0.145898034 Simplifying x = -0.145898034Subproblem 2
x + 3.5 = -3.354101966 Simplifying x + 3.5 = -3.354101966 Reorder the terms: 3.5 + x = -3.354101966 Solving 3.5 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.354101966 + -3.5 x = -3.354101966 + -3.5 Combine like terms: -3.354101966 + -3.5 = -6.854101966 x = -6.854101966 Simplifying x = -6.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.145898034, -6.854101966}Solution
x = {-0.145898034, -6.854101966}
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