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Simplifying 2x(x + -7) = 98 + -4x Reorder the terms: 2x(-7 + x) = 98 + -4x (-7 * 2x + x * 2x) = 98 + -4x (-14x + 2x2) = 98 + -4x Solving -14x + 2x2 = 98 + -4x Solving for variable 'x'. Reorder the terms: -98 + -14x + 4x + 2x2 = 98 + -4x + -98 + 4x Combine like terms: -14x + 4x = -10x -98 + -10x + 2x2 = 98 + -4x + -98 + 4x Reorder the terms: -98 + -10x + 2x2 = 98 + -98 + -4x + 4x Combine like terms: 98 + -98 = 0 -98 + -10x + 2x2 = 0 + -4x + 4x -98 + -10x + 2x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -98 + -10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + -5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + -5x + x2)' equal to zero and attempt to solve: Simplifying -49 + -5x + x2 = 0 Solving -49 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -5x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -5x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -5x + x2 = 0 + 49 -5x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -5x + x2 = 49 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 49 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 49 + 6.25 Combine like terms: 49 + 6.25 = 55.25 6.25 + -5x + x2 = 55.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -2.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -2.5 = 7.433034374 Simplifying x + -2.5 = 7.433034374 Reorder the terms: -2.5 + x = 7.433034374 Solving -2.5 + x = 7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 7.433034374 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 7.433034374 + 2.5 x = 7.433034374 + 2.5 Combine like terms: 7.433034374 + 2.5 = 9.933034374 x = 9.933034374 Simplifying x = 9.933034374Subproblem 2
x + -2.5 = -7.433034374 Simplifying x + -2.5 = -7.433034374 Reorder the terms: -2.5 + x = -7.433034374 Solving -2.5 + x = -7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -7.433034374 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -7.433034374 + 2.5 x = -7.433034374 + 2.5 Combine like terms: -7.433034374 + 2.5 = -4.933034374 x = -4.933034374 Simplifying x = -4.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.933034374, -4.933034374}Solution
x = {9.933034374, -4.933034374}
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