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Simplifying 7x2 + -49x + -28 = 0 Reorder the terms: -28 + -49x + 7x2 = 0 Solving -28 + -49x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-4 + -7x + x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-4 + -7x + x2)' equal to zero and attempt to solve: Simplifying -4 + -7x + x2 = 0 Solving -4 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -7x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -7x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7x + x2 = 0 + 4 -7x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -7x + x2 = 4 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 = 4 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 4 + 12.25 Combine like terms: 4 + 12.25 = 16.25 12.25 + -7x + x2 = 16.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -3.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -3.5 = 4.031128874 Simplifying x + -3.5 = 4.031128874 Reorder the terms: -3.5 + x = 4.031128874 Solving -3.5 + x = 4.031128874 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 = 4.031128874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.031128874 + 3.5 x = 4.031128874 + 3.5 Combine like terms: 4.031128874 + 3.5 = 7.531128874 x = 7.531128874 Simplifying x = 7.531128874Subproblem 2
x + -3.5 = -4.031128874 Simplifying x + -3.5 = -4.031128874 Reorder the terms: -3.5 + x = -4.031128874 Solving -3.5 + x = -4.031128874 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 = -4.031128874 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.031128874 + 3.5 x = -4.031128874 + 3.5 Combine like terms: -4.031128874 + 3.5 = -0.531128874 x = -0.531128874 Simplifying x = -0.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.531128874, -0.531128874}Solution
x = {7.531128874, -0.531128874}
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