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Simplifying 7x2 + -14x + -420 = 0 Reorder the terms: -420 + -14x + 7x2 = 0 Solving -420 + -14x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-60 + -2x + x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-60 + -2x + x2)' equal to zero and attempt to solve: Simplifying -60 + -2x + x2 = 0 Solving -60 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -2x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -2x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -2x + x2 = 0 + 60 -2x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -2x + x2 = 60 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 60 + 1 Reorder the terms: 1 + -2x + x2 = 60 + 1 Combine like terms: 60 + 1 = 61 1 + -2x + x2 = 61 Factor a perfect square on the left side: (x + -1)(x + -1) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -1) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -1 = 7.810249676 Simplifying x + -1 = 7.810249676 Reorder the terms: -1 + x = 7.810249676 Solving -1 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7.810249676 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.810249676 + 1 x = 7.810249676 + 1 Combine like terms: 7.810249676 + 1 = 8.810249676 x = 8.810249676 Simplifying x = 8.810249676Subproblem 2
x + -1 = -7.810249676 Simplifying x + -1 = -7.810249676 Reorder the terms: -1 + x = -7.810249676 Solving -1 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7.810249676 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.810249676 + 1 x = -7.810249676 + 1 Combine like terms: -7.810249676 + 1 = -6.810249676 x = -6.810249676 Simplifying x = -6.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.810249676, -6.810249676}Solution
x = {8.810249676, -6.810249676}
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