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Simplifying 4x2 = 28x + 42 Reorder the terms: 4x2 = 42 + 28x Solving 4x2 = 42 + 28x Solving for variable 'x'. Reorder the terms: -42 + -28x + 4x2 = 42 + 28x + -42 + -28x Reorder the terms: -42 + -28x + 4x2 = 42 + -42 + 28x + -28x Combine like terms: 42 + -42 = 0 -42 + -28x + 4x2 = 0 + 28x + -28x -42 + -28x + 4x2 = 28x + -28x Combine like terms: 28x + -28x = 0 -42 + -28x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -14x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -14x + 2x2)' equal to zero and attempt to solve: Simplifying -21 + -14x + 2x2 = 0 Solving -21 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + -7x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -7x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -7x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -7x + x2 = 0 + 10.5 -7x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -7x + x2 = 10.5 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 = 10.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 10.5 + 12.25 Combine like terms: 10.5 + 12.25 = 22.75 12.25 + -7x + x2 = 22.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (x + -3.5) equal to 4.769696007 and -4.769696007.Subproblem 1
x + -3.5 = 4.769696007 Simplifying x + -3.5 = 4.769696007 Reorder the terms: -3.5 + x = 4.769696007 Solving -3.5 + x = 4.769696007 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 = 4.769696007 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.769696007 + 3.5 x = 4.769696007 + 3.5 Combine like terms: 4.769696007 + 3.5 = 8.269696007 x = 8.269696007 Simplifying x = 8.269696007Subproblem 2
x + -3.5 = -4.769696007 Simplifying x + -3.5 = -4.769696007 Reorder the terms: -3.5 + x = -4.769696007 Solving -3.5 + x = -4.769696007 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 = -4.769696007 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.769696007 + 3.5 x = -4.769696007 + 3.5 Combine like terms: -4.769696007 + 3.5 = -1.269696007 x = -1.269696007 Simplifying x = -1.269696007Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.269696007, -1.269696007}Solution
x = {8.269696007, -1.269696007}
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