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Simplifying 4x2 + 28x = 400 Reorder the terms: 28x + 4x2 = 400 Solving 28x + 4x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 28x + 4x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 28x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-100 + 7x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-100 + 7x + x2)' equal to zero and attempt to solve: Simplifying -100 + 7x + x2 = 0 Solving -100 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 7x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 7x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 7x + x2 = 0 + 100 7x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 7x + x2 = 100 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 = 100 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 100 + 12.25 Combine like terms: 100 + 12.25 = 112.25 12.25 + 7x + x2 = 112.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (x + 3.5) equal to 10.59481005 and -10.59481005.Subproblem 1
x + 3.5 = 10.59481005 Simplifying x + 3.5 = 10.59481005 Reorder the terms: 3.5 + x = 10.59481005 Solving 3.5 + x = 10.59481005 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 = 10.59481005 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 10.59481005 + -3.5 x = 10.59481005 + -3.5 Combine like terms: 10.59481005 + -3.5 = 7.09481005 x = 7.09481005 Simplifying x = 7.09481005Subproblem 2
x + 3.5 = -10.59481005 Simplifying x + 3.5 = -10.59481005 Reorder the terms: 3.5 + x = -10.59481005 Solving 3.5 + x = -10.59481005 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 = -10.59481005 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -10.59481005 + -3.5 x = -10.59481005 + -3.5 Combine like terms: -10.59481005 + -3.5 = -14.09481005 x = -14.09481005 Simplifying x = -14.09481005Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.09481005, -14.09481005}Solution
x = {7.09481005, -14.09481005}
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